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2 4 Rataje 23 +245000.0 True 2 4 Rataje 44 +240000.0 True 2 2 Dębiec 48 +262000.0 True 2 4 Grunwald 60 +395000.0 True 4 1 Smochowice 69 +313000.0 True 2 4 Piątkowo 50 +409000.0 True 3 1 Malta 90 +599000.0 True 3 3 Grunwald 83 +289000.0 True 2 2 Jeżyce 42 +390000.0 True 3 3 Naramowice 48 +313000.0 True 2 4 Piątkowo 49 +375000.0 True 4 2 Centrum 72 +350000.0 True 3 1 Naramowice 51 +304140.0 False 3 5 Winogrady 18 +353275.0 False 2 14 Grunwald 74 +244071.0 False 2 1 Nowe 93 +348000.0 True 3 9 Rataje 65 +320000.0 True 3 4 Winogrady 53 +348000.0 True 3 9 Rataje 65 +348000.0 True 3 9 Rataje 65 +230000.0 True 2 1 Dębiec 37 +238000.0 True 2 2 Grunwald 37 +392000.0 True 4 0 Piątkowo 74 +380000.0 True 4 2 Piątkowo 74 +329000.0 True 2 4 Górczyn 20 +347000.0 True 3 1 Naramowice 47 +259900.0 True 2 6 Winogrady 38 +590000.0 True 5 3 Piątkowo 125 +320000.0 True 2 1 Naramowice 53 +432000.0 True 2 5 Centrum 40 +435000.0 True 3 1 Piątkowo 84 +389000.0 True 2 1 Podolany 46 +799999.0 True 3 1 Sołacz 90 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Grunwald 47 +755000.0 True 4 2 Łazarz 90 +319000.0 True 2 0 Górczyn 54 +380000.0 True 3 1 Łazarz 30 +530000.0 True 3 1 Piątkowo 76 +900000.0 True 3 2 Grunwald 112 +375000.0 True 3 8 Piątkowo 75 +576500.0 True 2 5 Centrum 50 +576500.0 True 2 5 Chwaliszewo 50 +438503.0 True 3 2 Centrum 57 +354454.0 False 2 3 Grunwald 17 +489780.0 False 4 2 Górczyn 63 +491520.0 False 4 1 Górczyn 92 +273875.5 False 2 1 Grunwald 13 +267000.0 True 2 2 Dębiec 35 +260000.0 True 2 2 Piątkowo 90 +587000.0 True 4 3 Łazarz 38 +460000.0 True 3 1 Naramowice 110 +695000.0 True 4 1 Rataje 70 +506657.0 True 4 11 Grunwald 73 +298250.0 True 2 5 Grunwald 38 +297421.0 True 2 2 Grunwald 24 +275000.0 True 2 9 Nowe 38 +267000.0 True 2 4 Nowe 70 +447000.0 True 3 4 Grunwald 20 +349900.0 True 3 4 Wilda 42 +360000.0 True 4 0 Centrum 66 +525000.0 True 4 3 Jeżyce 70 +450000.0 True 3 2 Strzeszyn 70 +690000.0 True 4 5 Górczyn 25 +334000.0 True 2 4 Sołacz 50 +240000.0 True 2 3 Jeżyce 43 +307000.0 True 3 2 Rataje 48 +307000.0 True 2 2 Rataje 48 +345000.0 True 3 8 Nowe 63 +333694.0 False 3 1 Podolany 32 +333694.0 False 3 1 Piątkowo 38 +299000.0 True 3 0 Grunwald 53 +389000.0 True 3 3 Stare 49 +310000.0 True 2 2 Centrum 74 +220000.0 True 2 0 Grunwald 50 +332800.0 True 2 1 Grunwald 52 +240000.0 True 2 2 Stare 38 +323206.0 False 2 2 Naramowice 50 +558745.0 False 3 3 Stare 62 +290000.0 True 2 6 Jeżyce 49 +285000.0 True 2 3 Piątkowo 49 +365000.0 True 3 1 Rataje 67 +263000.0 True 2 1 Rataje 47 +289000.0 True 2 2 Jeżyce 42 +265000.0 True 3 4 Grunwald 48 +310000.0 True 2 1 Nowe 40 +300000.0 True 3 2 Winogrady 48 +565964.0 True 2 5 Centrum 49 +747000.0 True 3 7 Rataje 84 +275000.0 True 2 0 Naramowice 50 +405000.0 True 4 2 Rataje 71 +491520.0 True 4 1 Górczyn 92 +363258.0 True 2 1 Górczyn 59 +305739.0 True 2 2 Górczyn 53 +399000.0 True 3 4 Piątkowo 69 +280000.0 True 2 1 Sołacz 38 +299900.0 True 2 0 Dębiec 48 +420000.0 True 2 3 Naramowice 59 +650000.0 True 4 8 Rataje 100 +329000.0 True 3 3 Wilda 82 +355000.0 True 3 2 Piątkowo 66 +375000.0 True 3 2 Rataje 79 +200000.0 True 3 4 Nowe 44 +315000.0 True 2 2 Zawady 52 +259000.0 True 2 3 Rataje 49 +379000.0 True 3 2 Podolany 56 +354454.0 True 2 3 Górczyn 17 +237000.0 True 2 10 Górczyn 38 +315000.0 True 2 2 Zawady 52 +379999.0 True 3 2 Wilda 67 +279000.0 True 2 1 Naramowice 52 +250000.0 True 2 4 Rataje 44 +620000.0 True 3 2 Naramowice 98 +450000.0 True 3 5 Grunwald 60 +290000.0 True 2 2 Dębiec 40 +393599.0 True 2 6 Winogrady 49 +289000.0 True 2 2 Nowe 48 +240000.0 True 2 8 Dębiec 37 +420000.0 True 2 5 Rataje 63 +800000.0 True 3 3 Chwaliszewo 70 +285000.0 True 2 2 Łazarz 52 +495000.0 True 3 0 Centrum 63 +289575.0 True 2 0 Jeżyce 43 +259000.0 True 2 5 Grunwald 46 +265000.0 True 2 4 Grunwald 43 +495000.0 True 5 1 Naramowice 98 +275000.0 True 2 0 Naramowice 50 +320000.0 True 2 3 Chwaliszewo 56 +360000.0 True 2 5 Grunwald 41 +360000.0 True 2 0 Winogrady 48 +750000.0 True 4 0 Kobylepole 105 +260000.0 True 2 0 Rataje 46 +260000.0 True 3 4 Centrum 44 +1050000.0 True 5 2 Centrum 161 +379000.0 True 2 0 Nowe 56 +560000.0 True 2 8 Grunwald 55 +335400.0 True 2 1 Łazarz 51 +290000.0 True 2 5 Winogrady 42 +235000.0 True 2 3 Winogrady 38 +300000.0 True 2 4 Winogrady 53 +399000.0 True 3 1 Winiary 66 +830000.0 True 3 1 Grunwald 91 +385500.0 True 2 6 Dębiec 38 +199000.0 True 5 0 Sołacz 129 +295000.0 True 2 4 Stare 33 +370000.0 True 4 11 Rataje 74 +335000.0 True 3 1 Piątkowo 63 +350000.0 True 3 7 Piątkowo 63 +380000.0 True 3 1 Łazarz 98 +184000.0 True 2 0 Grunwald 34 +855000.0 True 4 5 Jeżyce 96 +215000.0 True 2 0 Wilda 36 +495000.0 True 4 1 Naramowice 98 +250000.0 True 2 5 Nowe 50 +275000.0 True 3 7 Wilda 53 +409000.0 True 3 1 Malta 61 +200000.0 True 2 0 Głuszyna 52 +299000.0 True 3 3 Wilda 66 +490000.0 True 4 3 Sołacz 83 +245000.0 True 2 0 Stare 44 +950000.0 True 3 4 Nowe 99 +355000.0 True 2 3 Nowe 50 +380000.0 True 3 3 Łazarz 95 +525000.0 True 4 3 Jeżyce 104 +400000.0 True 2 3 Naramowice 50 +248000.0 True 2 10 Grunwald 42 +380000.0 True 3 0 Centrum 55 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3 1 Łazarz 64 +599000.0 True 3 3 Grunwald 60 +390000.0 True 3 2 Podolany 68 +450000.0 True 4 1 Grunwald 101 +313000.0 True 2 4 Piątkowo 49 +338000.0 True 3 3 Wilda 63 +285000.0 True 2 11 Winogrady 47 +270000.0 True 2 0 Grunwald 42 +360000.0 True 4 4 Jeżyce 60 +399000.0 True 2 3 Centrum 60 +619000.0 True 3 5 Jeżyce 69 +330000.0 True 2 1 Jeżyce 53 +1612000.0 True 7 5 Jeżyce 166 +399000.0 True 3 3 Centrum 50 +365000.0 True 2 1 Stare 50 +450000.0 True 3 0 Grunwald 75 +288000.0 True 3 4 Winogrady 47 +240000.0 True 2 16 Rataje 36 +326000.0 True 2 0 Jeżyce 55 +250000.0 True 2 4 Zawady 66 +288000.0 True 2 4 Naramowice 44 +289000.0 True 2 7 Winiary 49 +515000.0 True 3 0 Rataje 69 +428000.0 True 3 3 Centrum 43 +510000.0 True 5 1 Naramowice 98 +320000.0 True 2 2 Piątkowo 48 +659200.0 True 4 3 Łazarz 103 +499000.0 True 5 0 Grunwald 130 +240000.0 True 2 2 Dębiec 48 +495000.0 True 4 1 Naramowice 98 +320000.0 True 3 0 Rataje 56 +430000.0 True 3 2 Rataje 64 +409000.0 True 5 4 Winogrady 64 +415000.0 True 3 4 Łazarz 53 +359000.0 True 3 2 Rataje 65 +410000.0 True 2 5 Rataje 53 +479000.0 True 3 3 Nowe 83 +365000.0 True 4 3 Grunwald 68 +369000.0 True 2 3 Grunwald 64 +259000.0 True 2 2 Nowe 42 +250000.0 True 3 4 Dębiec 45 +299000.0 True 2 4 Nowe 47 +430000.0 True 2 1 Centrum 72 +275000.0 True 2 0 Dębiec 50 +950000.0 True 3 4 Nowe 99 +329000.0 True 3 7 Rataje 78 +380000.0 True 4 6 Piątkowo 73 +299000.0 True 2 5 Centrum 49 +265000.0 True 2 1 Wilda 44 +370000.0 True 2 13 Rataje 48 +370000.0 True 4 4 Piątkowo 76 +379000.0 True 3 1 Piątkowo 78 +299000.0 True 2 3 Grunwald 44 +379999.0 True 2 5 Jeżyce 61 +1000000.0 True 5 1 Jeżyce 128 +549000.0 True 3 2 Jeżyce 106 +335000.0 True 3 9 Nowe 65 +489000.0 True 3 0 Jeżyce 65 +379000.0 True 3 4 Rataje 63 +245000.0 True 3 0 Grunwald 45 +235000.0 True 2 0 Łazarz 52 +295555.0 True 2 1 Jeżyce 45 +224000.0 True 2 0 Górczyn 38 +315000.0 True 2 2 Winogrady 38 +429000.0 True 3 4 Nowe 79 +595000.0 True 3 0 Naramowice 94 +330000.0 True 3 0 Bonin 56 +275000.0 True 2 13 Rataje 49 +499000.0 True 4 2 Wilda 120 +287000.0 True 2 10 Winogrady 46 +280000.0 True 2 10 Piątkowo 46 +273875.0 True 2 1 Górczyn 13 +450000.0 True 3 0 Winogrady 70 +325000.0 True 3 4 Jeżyce 64 +299817.0 True 2 3 Górczyn 59 +295000.0 True 2 2 Naramowice 58 +380000.0 True 4 6 Piątkowo 73 +399000.0 True 3 4 Winogrady 65 +305000.0 True 3 3 Winogrady 48 +220000.0 True 2 3 Jeżyce 37 +285000.0 True 3 2 Antoninek 61 +238000.0 True 2 2 Grunwald 37 +200000.0 True 2 0 Rataje 30 +298000.0 True 2 5 Centrum 50 +391729.0 False 3 2 Winogrady 42 +347090.0 False 3 2 Winogrady 41 +285678.0 False 2 1 Winogrady 82 +321656.0 False 2 4 Winogrady 38 +312259.0 False 2 6 Winogrady 60 +347090.0 False 3 1 Winogrady 90 +355042.0 False 3 6 Jeżyce 96 +496573.0 False 3 2 Stare 78 +300680.0 False 2 2 Starołęka 54 +395000.0 True 4 4 Piątkowo 90 +771672.0 False 4 4 Górczyn 66 +399000.0 True 4 1 Szczepankowo 60 +340100.0 True 3 0 Szczepankowo 45 +225228.0 False 2 5 Rataje 91 +324387.0 False 2 9 Grunwald 49 +362459.0 False 3 0 Starołęka 80 +247705.0 False 2 1 Podolany 74 +339000.0 True 3 8 Nowe 78 +207000.0 True 2 2 Wilda 33 +295000.0 True 2 4 Grunwald 50 +324500.0 True 2 5 Wilda 65 +429000.0 True 3 4 Wilda 47 +399000.0 True 4 0 Szczepankowo 71 +411804.0 True 3 1 Winogrady 42 +282613.0 True 2 3 Winogrady 33 +235399.0 True 2 1 Winogrady 59 +265741.0 True 2 7 Winogrady 21 +323340.0 True 3 3 Winogrady 89 +293848.0 True 3 7 Winogrady 57 +337303.0 True 4 2 Winogrady 17 +470092.0 True 2 3 Centrum 21 +310000.0 True 2 0 Wilda 53 +365000.0 True 4 1 Nowe 54 +259000.0 True 2 6 Winogrady 38 +414225.0 True 3 3 Centrum 23 +489000.0 True 3 3 Grunwald 104 +350000.0 True 4 3 Grunwald 30 +325000.0 True 2 3 Rataje 20 +321845.0 False 3 1 Grunwald 55 +248000.0 True 2 14 Rataje 49 +286000.0 True 2 5 Centrum 64 +399000.0 True 3 4 Piątkowo 16 +289000.0 True 2 7 Winiary 80 +329000.0 True 3 11 Winogrady 50 +252723.0 False 2 1 Winogrady 43 +300680.0 False 2 2 Starołęka 54 +496573.0 False 3 2 Stare 78 +392181.0 False 3 4 Winogrady 42 +496573.0 False 3 2 Stare 78 +412438.0 False 3 2 Naramowice 17 +286000.0 True 2 5 Centrum 49 +269000.0 True 2 9 Rataje 49 +315000.0 True 2 1 Grunwald 61 +318390.0 True 3 3 Jeżyce 48 +242406.0 True 2 0 Jeżyce 36 +296278.0 True 3 2 Stare 49 +223747.0 True 2 0 Stare 37 +388755.0 True 4 5 Winogrady 65 +347095.0 True 3 1 Winogrady 57 +269000.0 True 2 1 Ogrody 50 +285000.0 True 2 9 Grunwald 50 +114642.0 True 2 0 Łazarz 46 +286000.0 True 2 5 Stare 64 +333693.0 True 3 1 Jeżyce 68 +435000.0 True 2 0 Świerczewo 60 +320000.0 True 4 1 Jeżyce 40 +395000.0 True 4 0 Grunwald 60 +353457.0 True 2 3 Stare 44 +267704.0 True 2 3 Grunwald 45 +245831.0 True 2 2 Grunwald 40 +391729.0 True 3 2 Winogrady 69 +240875.0 True 2 7 Stare 39 +424380.0 True 4 2 Nowe 74 +282996.0 True 2 0 Nowe 55 +285000.0 True 3 1 Rataje 48 +284618.0 False 2 3 Nowe 55 +512034.0 False 4 2 Winogrady 94 +284618.0 False 2 3 Nowe 55 +255404.0 False 2 6 Jeżyce 12 +315810.0 False 3 8 Winogrady 20 +282994.0 False 2 0 Starołęka 59 +637135.0 False 3 7 Grunwald 65 +754000.0 False 5 0 Morasko 42 +336000.0 True 3 0 Szczepankowo 85 +355000.0 True 2 3 Nowe 90 +475000.0 True 3 0 Rataje 73 +275000.0 True 3 4 Winogrady 60 +275000.0 True 3 4 Winogrady 70 +289000.0 True 2 7 Winogrady 80 +315000.0 True 3 0 Rataje 63 +260000.0 True 2 1 Łazarz 54 +370000.0 True 4 4 Piątkowo 76 +319990.0 True 2 3 Jeżyce 70 +156085.0 False 2 3 Głuszyna 45 +225228.0 False 2 5 Rataje 91 +308237.0 False 2 1 Nowe 85 +353275.0 False 2 14 Grunwald 74 +228144.0 False 3 2 Głuszyna 56 +156085.0 False 2 2 Głuszyna 45 +353275.0 False 2 14 Grunwald 74 +353275.0 False 2 14 Grunwald 74 +156085.0 False 2 3 Głuszyna 45 +156085.0 False 2 4 Nowe 54 +267702.0 False 2 3 Grunwald 22 +353275.0 False 2 14 Grunwald 74 +247705.0 False 2 1 Podolany 74 +315810.0 False 3 8 Winogrady 20 +370000.0 True 4 4 Stare 60 +265000.0 True 2 2 Stare 70 +304140.0 False 3 3 Winogrady 27 +394000.0 False 4 0 Szczepankowo 77 +287882.0 False 2 1 Starołęka 85 +729000.0 True 3 0 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45 +356251.0 True 3 14 Grunwald 57 +225290.0 True 2 7 Rataje 39 +333701.0 True 3 1 Jeżyce 68 +368568.0 True 3 4 Jeżyce 68 +285000.0 True 3 2 Antoninek 61 +300000.0 True 2 9 Strzeszyn 45 +299000.0 True 2 5 Centrum 50 +249000.0 True 2 2 Grunwald 46 +599000.0 True 4 5 Malta 84 +250000.0 True 2 4 Wilda 54 +341776.0 True 2 2 Stare 44 +238000.0 True 2 13 Rataje 49 +279000.0 True 3 1 Wilda 68 +430000.0 True 2 3 Jeżyce 58 +255000.0 True 2 1 Winogrady 38 +360000.0 True 3 1 Grunwald 49 +339000.0 True 2 1 Górczyn 45 +855000.0 True 3 3 Centrum 90 +1179000.0 True 3 2 Centrum 40 +2700000.0 True 3 2 Centrum 90 +1170000.0 True 3 3 Centrum 90 +368712.0 True 2 2 Centrum 90 +991380.0 True 4 1 Nowe 20 +250000.0 True 2 3 Dębiec 53 +249000.0 True 3 4 Rataje 53 +350000.0 True 2 4 Jeżyce 56 +285000.0 True 2 2 Centrum 52 +285000.0 True 2 2 Łazarz 52 +490000.0 True 4 2 Jeżyce 87 +429000.0 True 4 2 Grunwald 92 +211190.0 False 2 0 Podolany 78 +375529.0 False 2 3 Centrum 71 +225228.0 False 2 0 Rataje 71 +991380.0 False 5 1 Starołęka 94 +1156054.0 False 4 0 Stare 52 +288000.0 True 2 4 Naramowice 44 +820000.0 True 4 1 Grunwald 133 +370000.0 True 4 4 Piątkowo 76 +156085.0 False 2 0 Głuszyna 54 +156085.0 False 2 0 Głuszyna 54 +200460.0 False 2 0 Głuszyna 55 +200460.0 False 2 0 Głuszyna 55 +156085.0 False 2 0 Głuszyna 54 +156085.0 False 2 0 Głuszyna 54 +308237.0 False 2 1 Nowe 85 +225288.0 False 2 9 Rataje 91 +267702.0 False 2 3 Grunwald 22 +364000.0 True 3 4 Nowe 90 +280000.0 True 2 4 Winogrady 30 +349000.0 True 4 0 Rataje 84 +412000.0 True 4 0 Nowe 88 +490000.0 True 3 4 Piątkowo 82 +359602.0 True 3 5 Grunwald 58 +333025.0 True 2 1 Stare 45 +450000.0 True 2 3 Stare 62 +248000.0 True 2 2 Winogrady 80 +270000.0 True 3 10 Śródka 48 +239000.0 True 2 11 Stare 38 +225292.0 True 2 1 Rataje 39 +290970.0 True 2 4 Górczyn 70 +194500.0 True 2 3 Nowe 90 +712980.0 True 4 3 Centrum 102 +712980.0 True 5 2 Centrum 102 +855000.0 True 3 2 Centrum 72 +279000.0 True 2 6 Stare 49 +313830.0 True 2 4 Jeżyce 55 +325050.0 True 2 4 Jeżyce 25 +240158.0 True 2 0 Stare 39 +211190.0 True 2 0 Jeżyce 38 +333690.0 True 3 2 Jeżyce 68 +388751.0 True 4 5 Winogrady 65 +347091.0 True 3 1 Winogrady 57 +362450.0 True 3 1 Górczyn 90 +225288.91 True 2 6 Rataje 91 +225288.91 True 2 5 Rataje 91 +225288.91 True 2 1 Rataje 91 +392860.63 True 4 3 Winogrady 41 +364762.0 True 4 4 Winogrady 89 +316498.0 True 2 2 Centrum 77 +442002.0 True 2 3 Centrum 73 +276610.0 True 2 4 Centrum 80 +316355.0 True 2 4 Centrum 67 +280250.0 True 2 0 Górczyn 50 +327127.5 True 2 0 Centrum 50 +449000.0 False 5 0 Szczepankowo 68 +225288.0 False 2 1 Rataje 91 +286327.0 False 2 3 Naramowice 82 +365690.0 False 4 2 Naramowice 50 +389528.0 False 2 2 Stare 87 +481903.0 False 3 2 Stare 53 +349000.0 False 4 0 Szczepankowo 29 +347090.0 False 3 2 Naramowice 41 +534523.0 False 3 2 Stare 62 +412670.0 False 3 1 Naramowice 17 +285678.0 False 2 2 Naramowice 82 +263000.0 True 2 0 Wilda 75 +245000.0 True 2 2 Winogrady 20 +232410.0 True 2 0 Stare 38 +245488.0 True 2 0 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+ "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Uczenie maszynowe 2017/2018\n", + "# 1. Wprowadzenie. Regresja liniowa" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 1.1. Uczenie maszynowe – przykłady zastosowań" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Rozpoznawanie i rozumienie mowy" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "import IPython" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/jpeg": 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F8nEA51ocJsTbyQo6T0Mj6Dmhn3GuUv4tSehiFBzYyNG/GLfkHs7vja+dySQrBDGT4lkp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\nIlc9Vr97bPjNJMFNzYGQzXz0RgC53fG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Yd07FUebjmrlNNXNncwQQzxXYltX+GVAcA+RHgaX93ysm6cs4TeoHj5inNJc2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\nGJKt3s9/n/2qzXJ2e8CseEAO0dPWupbNGxMBjkWUbtjjH4G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UjbiMRZlWRWMYDHByNEoGlsg4I/hUS6V3o+O8IuFBGJ5bds7MBKiKAwH5xPtq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\n3DrEVYBZCoTPdnO+KmXwT3mhupoWikjhlg7ausikTKchj1g3GFcY7tY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OLS7ePoX2aGyn4v6/XBqqb6szoTK/6hP+GfgmQ1lNHC1r5mNcBqCVzrqymfRT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\nRvDKmJ0bjsvxrlHG+V2Vmhte/Ir5TSi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+ "text/html": [ + "\n", + " \n", + " " + ], + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "IPython.display.YouTubeVideo('SUbqykXVx0A', width=800, height=600)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 1.2. Czym jest uczenie maszynowe?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\n", + "\n", + "> Uczenie maszynowe to dziedzina nauki,\n", + "> która daje komputerom umiejętność uczenia się\n", + "> bez programowania ich _explicite_.\n", + "\n", + "> — Arthur Samuel, 1959" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\n", + "\n", + "> Mówimy, że program komputerowy **uczy się**\n", + "> z doświadczenia E w odniesieniu do zadania T i miary skuteczności P,\n", + "> jeżeli jego skuteczność wykonywania zadania T mierzona według P\n", + "> wzrasta z doświadczeniem E.\n", + "\n", + "> — Tom Mitchell, 1998" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\n", + "\n", + "Źródło: Drew Conway, http://drewconway.com/zia/2013/3/26/the-data-science-venn-diagram" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Uczenie maszynowe to:\n", + "\n", + "* doskonalenie działania dla pewnych zadań na podstawie doświadczenia" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* tworzenie systemów, które doskonalą swoje działania na podstawie przeszłych doświadczeń" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* zestaw metod, które potrafią w sposób automatyczny wykrywać wzorce w danych, a następnie używać wcześniej niezaobserwowanych wzorców do przewidywania przyszłych zjawisk" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Charakterystyczne cechy uczenia maszynowego:\n", + "\n", + "* „automatyzacja automatyzacji”\n", + "* komputer „sam się programuje”\n", + "* modelowanie danych zastępuje pisanie programu" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\n", + "\n", + "Źródło: https://recast.ai/blog/machine-learning-algorithms/" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 1.3. Metody uczenia maszynowego" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Z jakimi rodzajami zadań mamy do czynienia?\n", + "\n", + "* Uczenie nadzorowane\n", + " * Regresja\n", + " * Klasyfikacja\n", + "* Uczenie nienadzorowane\n", + " * Klastrowanie\n", + "* Uczenie przez wzmacnianie\n", + "* Systemy rekomendacyjne" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Klasyfikator\n", + "\n", + "* Klasyfikator to funkcja $h$, która przykładowi $x$ przyporządkowuje prognozowaną wartość $h(x)$.\n", + "* Jeżeli funkcja $h$ jest ciągła, to mówimy o zagadnieniu **regresji**.\n", + "* Jeżeli funkcja $h$ jest dyskretna, to mówimy o zagadnieniu **klasyfikacji**." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Algorytm uczący\n", + "\n", + "* Dane są przykładowe obserwacje $(X, y)$.\n", + "* Staramy się dobrać funkcję (klasyfikator) $h$ tak, żeby $h(x) \\sim y$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "W jaki sposób można określić, czy klasyfikator jest „dobry”?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Podział metod uczenia maszynowego\n", + "\n", + "> \\[Każdy algorytm uczenia maszynowego\\] stanowi kombinację dokładnie trzech składników.\n", + "> Te składniki to:\n", + "> * reprezentacja\n", + "> * ewaluacja\n", + "> * optymalizacja\n", + "\n", + "> — Pedro Domingos, “A Few Useful Things to Know about Machine Learning”" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Reprezentacja\n", + "\n", + "* drzewa decyzyjne\n", + "* regresja liniowa\n", + "* regresja logistyczna\n", + "* naiwny klasyfikator bayesowski\n", + "* algorytm $k$ najbliższych sąsiadów\n", + "* sieci neuronowe\n", + "* maszyny wektorów nośnych\n", + "* algorytmy genetyczne\n", + "* ..." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Ewaluacja\n", + "\n", + "* skuteczność (dokładność)\n", + "* precyzja i pokrycie\n", + "* błąd średniokwadratowy\n", + "* _information gain_\n", + "* _logistic loss_\n", + "* BLEU\n", + "* ..." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Optymalizacja\n", + "\n", + "* optymalizacja kombinatoryczna:\n", + " * wyszukiwanie zachłanne,\n", + " * _beam search_...\n", + "* optymalizacja ciągła:\n", + " * nieograniczona:\n", + " * metoda gradientu prostego,\n", + " * metoda Newtona...\n", + " * ograniczona:\n", + " * programowanie liniowe..." + ] + }, + { + "cell_type": "code", + "execution_count": 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\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Funkcje rysujące wykres kropkowy oraz prostą regresyjną\n", + "\n", + "def regdots(x, y): \n", + " fig = pl.figure(figsize=(16*.6, 9*.6))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + " ax.scatter(x, y, c='r', s=50, label='Dane')\n", + " \n", + " ax.set_xlabel(u'Wielkość miejscowości [dzies. tys. mieszk.]')\n", + " ax.set_ylabel(u'Dochód firmy [dzies. tys. dolarów]')\n", + " ax.margins(.05, .05)\n", + " pl.ylim(min(y) - 1, max(y) + 1)\n", + " pl.xlim(min(x) - 1, max(x) + 1)\n", + " return fig\n", + "\n", + "def regline(fig, fun, theta, x):\n", + " ax = fig.axes[0]\n", + " x0, x1 = min(x), max(x)\n", + " X = [x0, x1]\n", + " Y = [fun(theta, x) for x in X]\n", + " ax.plot(X, Y, linewidth='2',\n", + " label=(r'$y={theta0}{op}{theta1}x$'.format(\n", + " theta0=theta[0],\n", + " theta1=(theta[1] if theta[1] >= 0 else -theta[1]),\n", + " op='+' if theta[1] >= 0 else '-')))\n", + "\n", + "def legend(fig):\n", + " ax = fig.axes[0]\n", + " handles, labels = ax.get_legend_handles_labels()\n", + " # try-except block is a fix for a bug in Poly3DCollection\n", + " try:\n", + " fig.legend(handles, labels, fontsize='15', loc='lower right')\n", + " except AttributeError:\n", + " pass\n", + "\n", + "fig = regdots(x,y)\n", + "legend(fig)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Hipoteza: funkcja liniowa jednej zmiennej\n", + "\n", + "def h(theta, x):\n", + " return theta[0] + theta[1] * x" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przygotowanie interaktywnego wykresu\n", + "\n", + "sliderTheta01 = widgets.FloatSlider(min=-10, max=10, step=0.1, value=0, description=r'$\\theta_0$', width=300)\n", + "sliderTheta11 = widgets.FloatSlider(min=-5, max=5, step=0.1, value=0, description=r'$\\theta_1$', width=300)\n", + "\n", + "def slide1(theta0, theta1):\n", + " fig = regdots(x, y)\n", + " regline(fig, h, [theta0, theta1], x)\n", + " legend(fig)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "58798d3c3e2c4f14b9fc02d62f47f1da", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

Failed to display Jupyter Widget of type interactive.

\n", + "

\n", + " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", + " that the widgets JavaScript is still loading. If this message persists, it\n", + " likely means that the widgets JavaScript library is either not installed or\n", + " not enabled. See the Jupyter\n", + " Widgets Documentation for setup instructions.\n", + "

\n", + "

\n", + " If you're reading this message in another notebook frontend (for example, a static\n", + " rendering on GitHub or NBViewer),\n", + " it may mean that your frontend doesn't currently support widgets.\n", + "

\n" + ], + "text/plain": [ + "interactive(children=(FloatSlider(value=0.0, description='$\\\\theta_0$', max=10.0, min=-10.0), FloatSlider(value=0.0, description='$\\\\theta_1$', max=5.0, min=-5.0), Button(description='Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "widgets.interact_manual(slide1, theta0=sliderTheta01, theta1=sliderTheta11)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Funkcja kosztu" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Będziemy szukać takich parametrów $\\theta = \\left[\\begin{array}{c}\\theta_0\\\\ \\theta_1\\end{array}\\right]$, które minimalizują fukcję kosztu $J(\\theta)$:" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$ \\hat\\theta = \\mathop{\\arg\\min}_{\\theta} J(\\theta) $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$ \\theta \\in \\mathbb{R}^2, \\quad J \\colon \\mathbb{R}^2 \\to \\mathbb{R} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Błąd średniokwadratowy\n", + "#### (metoda najmniejszych kwadratów)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$ J(\\theta) \\, = \\, \\frac{1}{2m} \\sum_{i = 1}^{m} \\left( h_{\\theta} \\left( x^{(i)} \\right) - y^{(i)} \\right) ^2 $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "$$ J(\\theta_0, \\theta_1) \\, = \\, \\frac{1}{2m} \\sum_{i = 1}^{m} \\left( \\theta_0 + \\theta_1 x^{(i)} - y^{(i)} \\right) ^2 $$" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [], + "source": [ + "def J(h, theta, x, y):\n", + " m = len(y)\n", + " return 1.0 / (2 * m) * sum((h(theta, x[i]) - y[i])**2 for i in range(m))" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Oblicz wartość funkcji kosztu i pokaż na wykresie\n", + "\n", + "def regline(fig, fun, theta, x, y):\n", + " ax = fig.axes[0]\n", + " x0, x1 = min(x), max(x)\n", + " X = [x0, x1]\n", + " Y = [fun(theta, x) for x in X]\n", + " cost = J(fun, theta, x, y)\n", + " ax.plot(X, Y, linewidth='2',\n", + " label=(r'$y={theta0}{op}{theta1}x, \\; J(\\theta)={cost:.3}$'.format(\n", + " theta0=theta[0],\n", + " theta1=(theta[1] if theta[1] >= 0 else -theta[1]),\n", + " op='+' if theta[1] >= 0 else '-',\n", + " cost=cost)))\n", + "\n", + "sliderTheta02 = widgets.FloatSlider(min=-10, max=10, step=0.1, value=0, description=r'$\\theta_0$', width=300)\n", + "sliderTheta12 = widgets.FloatSlider(min=-5, max=5, step=0.1, value=0, description=r'$\\theta_1$', width=300)\n", + "\n", + "def slide2(theta0, theta1):\n", + " fig = regdots(x, y)\n", + " regline(fig, h, [theta0, theta1], x, y)\n", + " legend(fig)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "c380a0076fb4480a9f9a0eb4f5fba756", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

Failed to display Jupyter Widget of type interactive.

\n", + "

\n", + " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", + " that the widgets JavaScript is still loading. If this message persists, it\n", + " likely means that the widgets JavaScript library is either not installed or\n", + " not enabled. See the Jupyter\n", + " Widgets Documentation for setup instructions.\n", + "

\n", + "

\n", + " If you're reading this message in another notebook frontend (for example, a static\n", + " rendering on GitHub or NBViewer),\n", + " it may mean that your frontend doesn't currently support widgets.\n", + "

\n" + ], + "text/plain": [ + "interactive(children=(FloatSlider(value=0.0, description='$\\\\theta_0$', max=10.0, min=-10.0), FloatSlider(value=0.0, description='$\\\\theta_1$', max=5.0, min=-5.0), Button(description='Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "widgets.interact_manual(slide2, theta0=sliderTheta02, theta1=sliderTheta12)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Funkcja kosztu jako funkcja zmiennej $\\theta$" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wykres funkcji kosztu dla ustalonego theta_1=1.0\n", + "\n", + "def costfun(fun, x, y):\n", + " return lambda theta: J(fun, theta, x, y)\n", + "\n", + "def costplot(hypothesis, x, y, theta1=1.0):\n", + " fig = pl.figure(figsize=(16*.6, 9*.6))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + " ax.set_xlabel(r'$\\theta_0$')\n", + " ax.set_ylabel(r'$J(\\theta)$')\n", + " j = costfun(hypothesis, x, y)\n", + " fun = lambda theta0: j([theta0, theta1])\n", + " X = np.arange(-10, 10, 0.1)\n", + " Y = [fun(x) for x in X]\n", + " ax.plot(X, Y, linewidth='2', label=(r'$J(\\theta_0, {theta1})$'.format(theta1=theta1)))\n", + " return fig\n", + "\n", + "def slide3(theta1):\n", + " fig = costplot(h, x, y, theta1)\n", + " legend(fig)\n", + "\n", + "sliderTheta13 = widgets.FloatSlider(min=-5, max=5, step=0.1, value=1.0, description=r'$\\theta_1$', width=300)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "1b675985144a43d0997c79ada18bb446", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

Failed to display Jupyter Widget of type interactive.

\n", + "

\n", + " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", + " that the widgets JavaScript is still loading. If this message persists, it\n", + " likely means that the widgets JavaScript library is either not installed or\n", + " not enabled. See the Jupyter\n", + " Widgets Documentation for setup instructions.\n", + "

\n", + "

\n", + " If you're reading this message in another notebook frontend (for example, a static\n", + " rendering on GitHub or NBViewer),\n", + " it may mean that your frontend doesn't currently support widgets.\n", + "

\n" + ], + "text/plain": [ + "interactive(children=(FloatSlider(value=1.0, description='$\\\\theta_1$', max=5.0, min=-5.0), Button(description='Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "widgets.interact_manual(slide3, theta1=sliderTheta13)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wykres funkcji kosztu względem theta_0 i theta_1\n", + "\n", + "from mpl_toolkits.mplot3d import Axes3D\n", + "import pylab\n", + "\n", + "%matplotlib inline\n", + "\n", + "def costplot3d(hypothesis, x, y, show_gradient=False):\n", + " fig = pl.figure(figsize=(16*.6, 9*.6))\n", + " ax = fig.add_subplot(111, projection='3d')\n", + " fig.subplots_adjust(left=0.0, right=1.0, bottom=0.0, top=1.0)\n", + " ax.set_xlabel(r'$\\theta_0$')\n", + " ax.set_ylabel(r'$\\theta_1$')\n", + " ax.set_zlabel(r'$J(\\theta)$')\n", + " \n", + " j = lambda theta0, theta1: costfun(hypothesis, x, y)([theta0, theta1])\n", + " X = np.arange(-10, 10.1, 0.1)\n", + " Y = np.arange(-1, 4.1, 0.1)\n", + " X, Y = np.meshgrid(X, Y)\n", + " Z = np.matrix([[J(hypothesis, [theta0, theta1], x, y) \n", + " for theta0, theta1 in zip(xRow, yRow)] \n", + " for xRow, yRow in zip(X, Y)])\n", + " \n", + " ax.plot_surface(X, Y, Z, rstride=2, cstride=8, linewidth=0.5,\n", + " alpha=0.5, cmap='jet', zorder=0,\n", + " label=r\"$J(\\theta)$\")\n", + " ax.view_init(elev=20., azim=-150)\n", + "\n", + " ax.set_xlim3d(-10, 10);\n", + " ax.set_ylim3d(-1, 4);\n", + " ax.set_zlim3d(-100, 800);\n", + "\n", + " N = range(0, 800, 20)\n", + " pl.contour(X, Y, Z, N, zdir='z', offset=-100, cmap='coolwarm', alpha=1)\n", + " \n", + " ax.plot([-3.89578088] * 2,\n", + " [ 1.19303364] * 2,\n", + " [-100, 4.47697137598], \n", + " color='red', alpha=1, linewidth=1.3, zorder=100, linestyle='dashed',\n", + " label=r'minimum: $J(-3.90, 1.19) = 4.48$')\n", + " ax.scatter([-3.89578088] * 2,\n", + " [ 1.19303364] * 2,\n", + " [-100, 4.47697137598], \n", + " c='r', s=80, marker='x', alpha=1, linewidth=1.3, zorder=100, \n", + " label=r'minimum: $J(-3.90, 1.19) = 4.48$')\n", + " \n", + " if show_gradient:\n", + " ax.plot([3.0, 1.1],\n", + " [3.0, 2.4],\n", + " [263.0, 125.0], \n", + " color='green', alpha=1, linewidth=1.3, zorder=100)\n", + " ax.scatter([3.0],\n", + " [3.0],\n", + " [263.0], \n", + " c='g', s=30, marker='D', alpha=1, linewidth=1.3, zorder=100)\n", + "\n", + " ax.margins(0,0,0)\n", + " fig.tight_layout()" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + 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"display_data" + } + ], + "source": [ + "costplot3d(h, x, y)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def costplot2d(hypothesis, x, y, gradient_values=[], nohead=False):\n", + " fig = pl.figure(figsize=(16*.6, 9*.6))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + " ax.set_xlabel(r'$\\theta_0$')\n", + " ax.set_ylabel(r'$\\theta_1$')\n", + " \n", + " j = lambda theta0, theta1: costfun(hypothesis, x, y)([theta0, theta1])\n", + " X = np.arange(-10, 10.1, 0.1)\n", + " Y = np.arange(-1, 4.1, 0.1)\n", + " X, Y = np.meshgrid(X, Y)\n", + " Z = np.matrix([[J(hypothesis, [theta0, theta1], x, y) \n", + " for theta0, theta1 in zip(xRow, yRow)] \n", + " for xRow, yRow in zip(X, Y)])\n", + " \n", + " N = range(0, 800, 20)\n", + " pl.contour(X, Y, Z, N, cmap='coolwarm', alpha=1)\n", + "\n", + " ax.scatter([-3.89578088], [1.19303364], c='r', s=80, marker='x',\n", + " label=r'minimum: $J(-3.90, 1.19) = 4.48$')\n", + " \n", + " if len(gradient_values) > 0:\n", + " prev_theta = gradient_values[0][1]\n", + " ax.scatter([prev_theta[0]], [prev_theta[1]],\n", + " c='g', s=30, marker='D', zorder=100)\n", + " for cost, theta in gradient_values[1:]:\n", + " dtheta = [theta[0] - prev_theta[0], theta[1] - prev_theta[1]]\n", + " ax.arrow(prev_theta[0], prev_theta[1], dtheta[0], dtheta[1], \n", + " color='green', \n", + " head_width=(0.0 if nohead else 0.1), \n", + " head_length=(0.0 if nohead else 0.2),\n", + " zorder=100)\n", + " prev_theta = theta\n", + " \n", + " return fig" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " 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Metoda gradientu prostego" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Metoda gradientu prostego\n", + "Metoda znajdowania minimów lokalnych." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Idea:\n", + " * Zacznijmy od dowolnego $\\theta$.\n", + " * Zmieniajmy powoli $\\theta$ tak, aby zmniejszać $J(\\theta)$, aż w końcu znajdziemy minimum." + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " 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"slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przykładowe wartości kolejnych przybliżeń (sztuczne)\n", + "\n", + "gv = [[_, [3.0, 3.0]], [_, [2.6, 2.4]], [_, [2.2, 2.0]], [_, [1.6, 1.6]], [_, [0.4, 1.2]]]\n", + "\n", + "# Przygotowanie interaktywnego wykresu\n", + "\n", + "sliderSteps1 = widgets.IntSlider(min=0, max=3, step=1, value=0, description='kroki', width=300)\n", + "\n", + "def slide4(steps):\n", + " costplot2d(h, x, y, gradient_values=gv[:steps+1])" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "e9b6665115b748edb457981078f0042c", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

Failed to display Jupyter Widget of type interactive.

\n", + "

\n", + " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", + " that the widgets JavaScript is still loading. If this message persists, it\n", + " likely means that the widgets JavaScript library is either not installed or\n", + " not enabled. See the Jupyter\n", + " Widgets Documentation for setup instructions.\n", + "

\n", + "

\n", + " If you're reading this message in another notebook frontend (for example, a static\n", + " rendering on GitHub or NBViewer),\n", + " it may mean that your frontend doesn't currently support widgets.\n", + "

\n" + ], + "text/plain": [ + "interactive(children=(IntSlider(value=0, description='kroki', max=3), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "widgets.interact(slide4, steps=sliderSteps1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Metoda gradientu prostego\n", + "W każdym kroku będziemy aktualizować parametry $\\theta_j$:\n", + "\n", + "$$ \\theta_j := \\theta_j - \\alpha \\frac{\\partial}{\\partial \\theta_j} J(\\theta) \\quad \\mbox{ dla każdego } j $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Współczynnik $\\alpha$ nazywamy *długością kroku* lub *współczynnikiem szybkości uczenia* (_learning rate_)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "$$ \\begin{array}{rcl}\n", + "\\dfrac{\\partial}{\\partial \\theta_j} J(\\theta)\n", + " & = & \\dfrac{\\partial}{\\partial \\theta_j} \\dfrac{1}{2m} \\displaystyle\\sum_{i = 1}^{m} \\left( h_{\\theta} \\left( x^{(i)} \\right) - y^{(i)} \\right) ^2 \\\\\n", + " & = & 2 \\cdot \\dfrac{1}{2m} \\displaystyle\\sum_{i=1}^m \\left( h_\\theta \\left( x^{(i)} \\right) - y^{(i)} \\right) \\cdot \\dfrac{\\partial}{\\partial\\theta_j} \\left( h_\\theta \\left( x^{(i)} \\right) - y^{(i)} \\right) \\\\\n", + " & = & \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_\\theta \\left( x^{(i)} \\right) - y^{(i)} \\right) \\cdot \\dfrac{\\partial}{\\partial\\theta_j} \\left( \\displaystyle\\sum_{i=0}^n \\theta_i x_i^{(i)} - y^{(i)} \\right)\\\\\n", + " & = & \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_\\theta \\left( x^{(i)} \\right) -y^{(i)} \\right) x_j^{(i)} \\\\\n", + "\\end{array} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Czyli dla regresji liniowej jednej zmiennej:\n", + "\n", + "$$ h_\\theta(x) = \\theta_0 + \\theta_1x $$\n", + "\n", + "w każdym kroku będziemy aktualizować:\n", + "\n", + "$$\n", + "\\begin{array}{rcl}\n", + "\\theta_0 & := & \\theta_0 - \\alpha \\, \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_\\theta(x^{(i)})-y^{(i)} \\right) \\\\ \n", + "\\theta_1 & := & \\theta_1 - \\alpha \\, \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_\\theta(x^{(i)})-y^{(i)} \\right) x^{(i)}\\\\ \n", + "\\end{array}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "###### Uwaga!\n", + " * W każdym kroku aktualizujemy *jednocześnie* $\\theta_0$ i $\\theta_1$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + " * Kolejne kroki wykonujemy aż uzyskamy zbieżność" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Metoda gradientu prostego – implementacja" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wyświetlanie macierzy w LaTeX-u\n", + "\n", + "def LatexMatrix(matrix):\n", + " ltx = r'\\left[\\begin{array}'\n", + " m, n = matrix.shape\n", + " ltx += '{' + (\"r\" * n) + '}'\n", + " for i in range(m):\n", + " ltx += r\" & \".join([('%.4f' % j.item()) for j in matrix[i]]) + r\" \\\\ \"\n", + " ltx += r'\\end{array}\\right]'\n", + " return ltx" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [], + "source": [ + "def gradient_descent(h, cost_fun, theta, x, y, alpha, eps):\n", + " current_cost = cost_fun(h, theta, x, y)\n", + " log = [[current_cost, theta]] # log przechowuje wartości kosztu i parametrów\n", + " m = len(y)\n", + " while True:\n", + " new_theta = [\n", + " theta[0] - alpha/float(m) * sum(h(theta, x[i]) - y[i]\n", + " for i in range(m)), \n", + " theta[1] - alpha/float(m) * sum((h(theta, x[i]) - y[i]) * x[i]\n", + " for i in range(m))]\n", + " theta = new_theta # jednoczesna aktualizacja - używamy zmiennej tymaczasowej\n", + " try:\n", + " current_cost, prev_cost = cost_fun(h, theta, x, y), current_cost\n", + " except OverflowError:\n", + " break \n", + " if abs(prev_cost - current_cost) <= eps:\n", + " break \n", + " log.append([current_cost, theta])\n", + " return theta, log" + ] + }, + { + "cell_type": "code", + "execution_count": 67, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$$\\large\\textrm{Wynik:}\\quad \\theta = \\left[\\begin{array}{r}-3.5074 \\\\ 1.1540 \\\\ \\end{array}\\right] \\quad J(\\theta) = 4.4908 \\quad \\textrm{po 644 iteracjach}$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "best_theta, log = gradient_descent(h, J, [0.0, 0.0], x, y, alpha=0.02, eps=0.0001)\n", + "\n", + "display(Math(r'\\large\\textrm{Wynik:}\\quad \\theta = ' + \n", + " LatexMatrix(np.matrix(best_theta).reshape(2,1)) + \n", + " (r' \\quad J(\\theta) = %.4f' % log[-1][0]) \n", + " + r' \\quad \\textrm{po %d iteracjach}' % len(log))) " + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przygotowanie interaktywnego wykresu\n", + "\n", + "sliderSteps2 = widgets.IntSlider(min=0, max=500, step=1, value=1, description='kroki', width=300)\n", + "\n", + "def slide5(steps):\n", + " costplot2d(h, x, y, gradient_values=log[:steps+1], nohead=True)" + ] + }, + { + "cell_type": "code", + "execution_count": 69, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "fc6dd6fa531b4d8eac47c456831f61a4", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

Failed to display Jupyter Widget of type interactive.

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\n", + " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", + " that the widgets JavaScript is still loading. If this message persists, it\n", + " likely means that the widgets JavaScript library is either not installed or\n", + " not enabled. See the Jupyter\n", + " Widgets Documentation for setup instructions.\n", + "

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\n" + ], + "text/plain": [ + "interactive(children=(IntSlider(value=1, description='kroki', max=500), Button(description='Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 69, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "widgets.interact_manual(slide5, steps=sliderSteps2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Współczynnik $\\alpha$ (długość kroku)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + " * Jeżeli długość kroku jest zbyt mała, algorytm może działać zbyt wolno." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + " * Jeżeli długość kroku jest zbyt duża, algorytm może nie być zbieżny." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 1.6. Regresja liniowa wielu zmiennych" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Przykład – ceny mieszkań" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "y : price x1: isNew x2: rooms x3: floor x4: location x5: sqrMetres\n", + "476118.0 False 3 1 Centrum 78 \n", + "459531.0 False 3 2 Sołacz 62 \n", + "411557.0 False 3 0 Sołacz 15 \n", + "496416.0 False 4 0 Sołacz 14 \n", + "406032.0 False 3 0 Sołacz 15 \n", + "450026.0 False 3 1 Naramowice 80 \n", + "571229.15 False 2 4 Wilda 39 \n", + "325000.0 False 3 1 Grunwald 54 \n", + "268229.0 False 2 1 Grunwald 90 \n" + ] + } + ], + "source": [ + "reader = csv.reader(open('data02.tsv'), delimiter='\\t')\n", + "for i, row in enumerate(list(reader)[:10]):\n", + " if i == 0:\n", + " print(' '.join(['{}: {:8}'.format('x' + str(j) if j > 0 else 'y ', entry)\n", + " for j, entry in enumerate(row)]))\n", + " else:\n", + " print(' '.join(['{:12}'.format(entry) for entry in row]))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$ x^{(2)} = ({\\rm \"False\"}, 3, 2, {\\rm \"Sołacz\"}, 62), \\quad x_3^{(2)} = 2 $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Hipoteza" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "W naszym przypadku:\n", + "\n", + "$$ h_\\theta(x) = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\theta_3 x_3 + \\theta_4 x_4 + \\theta_5 x_5 $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "W ogólności:\n", + "\n", + "$$ h_\\theta(x) = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\ldots + \\theta_n x_n $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Jeżeli zdefiniujemy $x_0 = 1$:\n", + "\n", + "$$\n", + "\\begin{array}{rcl}\n", + "h_\\theta(x)\n", + " & = & \\theta_0 x_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\ldots + \\theta_n x_n \\\\\n", + " & = & \\displaystyle\\sum_{i=0}^{n} \\theta_i x_i \\\\\n", + " & = & \\theta^T \\, x \\\\\n", + " & = & x^T \\, \\theta \\\\\n", + "\\end{array}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Metoda gradientu prostego – notacja macierzowa" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$\n", + "X=\\left[\\begin{array}{cc}\n", + "1 & \\left( \\vec x^{(1)} \\right)^T \\\\\n", + "1 & \\left( \\vec x^{(2)} \\right)^T \\\\\n", + "\\vdots & \\vdots\\\\\n", + "1 & \\left( \\vec x^{(m)} \\right)^T \\\\\n", + "\\end{array}\\right] \n", + "= \\left[\\begin{array}{cccc}\n", + "1 & x_1^{(1)} & \\cdots & x_n^{(1)} \\\\\n", + "1 & x_1^{(2)} & \\cdots & x_n^{(2)} \\\\\n", + "\\vdots & \\vdots & \\ddots & \\vdots\\\\\n", + "1 & x_1^{(m)} & \\cdots & x_n^{(m)} \\\\\n", + "\\end{array}\\right]\n", + "\\quad\n", + "\\vec{y} = \n", + "\\left[\\begin{array}{c}\n", + "y^{(1)}\\\\\n", + "y^{(2)}\\\\\n", + "\\vdots\\\\\n", + "y^{(m)}\\\\\n", + "\\end{array}\\right]\n", + "\\quad\n", + "\\theta = \\left[\\begin{array}{c}\n", + "\\theta_0\\\\\n", + "\\theta_1\\\\\n", + "\\vdots\\\\\n", + "\\theta_n\\\\\n", + "\\end{array}\\right]\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wczytwanie danych z pliku za pomocą numpy\n", + "# Wersje macierzowe funkcji rysowania wykresów punktowych oraz krzywej regresyjnej\n", + "\n", + "data = np.loadtxt('data01.csv', delimiter=',')\n", + "m, n_plus_1 = data.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data[:, 0:n].reshape(m, n)\n", + "\n", + "# Dodaj kolumnę jedynek do macierzy\n", + "XMx = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n", + "yMx = np.matrix(data[:, 1]).reshape(m, 1)\n", + "\n", + "def hMx(theta, X):\n", + " return X * theta\n", + "\n", + "def regdotsMx(X, y): \n", + " fig = pl.figure(figsize=(16*.6, 9*.6))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + " ax.scatter([X[:, 1]], [y], c='r', s=50, label='Dane')\n", + " \n", + " ax.set_xlabel('Populacja')\n", + " ax.set_ylabel('Zysk')\n", + " ax.margins(.05, .05)\n", + " pl.ylim(y.min() - 1, y.max() + 1)\n", + " pl.xlim(np.min(X[:, 1]) - 1, np.max(X[:, 1]) + 1)\n", + " return fig\n", + "\n", + "def reglineMx(fig, fun, theta, X):\n", + " ax = fig.axes[0]\n", + " x0, x1 = np.min(X[:, 1]), np.max(X[:, 1])\n", + " L = [x0, x1]\n", + " LX = np.matrix([1, x0, 1, x1]).reshape(2, 2)\n", + " ax.plot(L, fun(theta, LX), linewidth='2',\n", + " label=(r'$y={theta0:.2}{op}{theta1:.2}x$'.format(\n", + " theta0=float(theta[0][0]),\n", + " theta1=(float(theta[1][0]) if theta[1][0] >= 0 else float(-theta[1][0])),\n", + " op='+' if theta[1][0] >= 0 else '-')))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Funkcja kosztu – notacja macierzowa" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$J(\\theta)=\\dfrac{1}{2|\\vec y|}\\left(X\\theta-\\vec{y}\\right)^T\\left(X\\theta-\\vec{y}\\right)$$ \n" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$$\\Large J(\\theta) = 4.5885$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Wersja macierzowa funkcji kosztu\n", + "\n", + "def JMx(theta,X,y):\n", + " m = len(y)\n", + " J = 1.0 / (2.0 * m) * ((X * theta - y) . T * ( X * theta - y))\n", + " return J.item()\n", + "\n", + "thetaMx = np.matrix([-5, 1.3]).reshape(2, 1) \n", + "\n", + "cost = JMx(thetaMx,XMx,yMx) \n", + "display(Math(r'\\Large J(\\theta) = %.4f' % cost))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Gradient – notacja macierzowa" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$\\nabla J(\\theta) = \\frac{1}{|\\vec y|} X^T\\left(X\\theta-\\vec y\\right)$$" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$$\\large \\theta = \\left[\\begin{array}{r}-5.0000 \\\\ 1.3000 \\\\ \\end{array}\\right]\\quad\\large \\nabla J(\\theta) = \\left[\\begin{array}{r}-0.2314 \\\\ -0.3027 \\\\ \\end{array}\\right]$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Wersja macierzowa gradientu funkcji kosztu\n", + "\n", + "def dJMx(theta,X,y):\n", + " return 1.0 / len(y) * (X.T * (X * theta - y)) \n", + "\n", + "thetaMx2 = np.matrix([-5, 1.3]).reshape(2, 1)\n", + "\n", + "display(Math(r'\\large \\theta = ' + LatexMatrix(thetaMx2) + \n", + " r'\\quad' + r'\\large \\nabla J(\\theta) = ' \n", + " + LatexMatrix(dJMx(thetaMx2,XMx,yMx))))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Algorytm gradientu prostego – notacja macierzowa" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$ \\theta := \\theta - \\alpha \\, \\nabla J(\\theta) $$" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$$\\large\\textrm{Wynik:}\\quad \\theta = \\left[\\begin{array}{r}-3.7217 \\\\ 1.1755 \\\\ \\end{array}\\right] \\quad J(\\theta) = 4.4797 \\quad \\textrm{po 1734 iteracjach}$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Implementacja algorytmu gradientu prostego za pomocą numpy i macierzy\n", + "\n", + "def GDMx(fJ, fdJ, theta, X, y, alpha=0.1, eps=10**-3):\n", + " current_cost = fJ(theta, X, y)\n", + " log = [[current_cost, theta]]\n", + " while True:\n", + " theta = theta - alpha * fdJ(theta, X, y) # implementacja wzoru\n", + " current_cost, prev_cost = fJ(theta, X, y), current_cost\n", + " if abs(prev_cost - current_cost) <= eps:\n", + " break\n", + " log.append([current_cost, theta]) \n", + " return theta, log\n", + "\n", + "thetaStartMx = np.matrix([0, 0]).reshape(2, 1)\n", + "\n", + "# Zmieniamy wartości alpha (rozmiar kroku) oraz eps (kryterium stopu)\n", + "thetaBestMx, log = GDMx(JMx, dJMx, thetaStartMx, \n", + " XMx, yMx, alpha=0.01, eps=0.00001)\n", + "\n", + "######################################################################\n", + "display(Math(r'\\large\\textrm{Wynik:}\\quad \\theta = ' + \n", + " LatexMatrix(thetaBestMx) + \n", + " (r' \\quad J(\\theta) = %.4f' % log[-1][0]) \n", + " + r' \\quad \\textrm{po %d iteracjach}' % len(log))) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 1.7. Metoda gradientu prostego w praktyce" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Kryterium stopu" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Na wykresie zobaczymy porównanie regresji dla różnych wartości `eps`" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", 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"text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = regdotsMx(XMx, yMx)\n", + "theta_e1, log1 = GDMx(JMx, dJMx, thetaStartMx, XMx, yMx, alpha=0.01, eps=0.01)\n", + "reglineMx(fig, hMx, theta_e1, XMx)\n", + "theta_e2, log2 = GDMx(JMx, dJMx, thetaStartMx, XMx, yMx, alpha=0.01, eps=0.000001)\n", + "reglineMx(fig, hMx, theta_e2, XMx)\n", + "legend(fig)" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$$\\theta_{10^{-2}} = \\left[\\begin{array}{r}0.0511 \\\\ 0.7957 \\\\ \\end{array}\\right]\\quad\\theta_{10^{-6}} = \\left[\\begin{array}{r}-3.8407 \\\\ 1.1875 \\\\ \\end{array}\\right]$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "display(Math(r'\\theta_{10^{-2}} = ' + LatexMatrix(theta_e1) +\n", + " r'\\quad\\theta_{10^{-6}} = ' + LatexMatrix(theta_e2)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Długość kroku ($\\alpha$)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Jak zmienia się koszt w kolejnych krokach w zależności od alfa\n", + "\n", + "def costchangeplot(logs):\n", + " fig = pl.figure(figsize=(16*.6, 9*.6))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + " ax.set_xlabel('krok')\n", + " ax.set_ylabel(r'$J(\\theta)$')\n", + "\n", + " X = np.arange(0, 500, 1)\n", + " Y = [logs[step][0] for step in X]\n", + " ax.plot(X, Y, linewidth='2', label=(r'$J(\\theta)$'))\n", + " return fig\n", + "\n", + "def slide7(alpha):\n", + " best_theta, log = gradient_descent(h, J, [0.0, 0.0], x, y, alpha=alpha, eps=0.0001)\n", + " fig = costchangeplot(log)\n", + " legend(fig)\n", + "\n", + "sliderAlpha1 = widgets.FloatSlider(min=0.01, max=0.03, step=0.001, value=0.02, description=r'$\\alpha$', width=300)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "8f617b06eebc49168e4b8daac54528cd", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

Failed to display Jupyter Widget of type interactive.

\n", + "

\n", + " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", + " that the widgets JavaScript is still loading. If this message persists, it\n", + " likely means that the widgets JavaScript library is either not installed or\n", + " not enabled. See the Jupyter\n", + " Widgets Documentation for setup instructions.\n", + "

\n", + "

\n", + " If you're reading this message in another notebook frontend (for example, a static\n", + " rendering on GitHub or NBViewer),\n", + " it may mean that your frontend doesn't currently support widgets.\n", + "

\n" + ], + "text/plain": [ + "interactive(children=(FloatSlider(value=0.02, description='$\\\\alpha$', max=0.03, min=0.01, step=0.001), Button(description='Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 33, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "widgets.interact_manual(slide7, alpha=sliderAlpha1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 1.8 Regresja liniowa – dodatek\n", + "### Regresja liniowa za pomocą macierzy normalnej" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Zamiast korzystać z algorytmu gradientu prostego\n", + "możemy bezpośrednio obliczyć minimum $J(\\theta)$ dla regresji liniowej ze wzoru: \n", + "\n", + "$$ \\theta = \\left( X^T X \\right)^{-1} \\, X^T \\, \\vec y $$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15rc1" + }, + "livereveal": { + "start_slideshow_at": "selected", + "theme": "amu" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/w1/zumz181b.pdf b/w1/zumz181b.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f4741bb280c98c5b97094522200843fa416098f9 GIT binary patch literal 734979 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True 4 4 Stare 85 +270000.0 True 2 16 Rataje 49 +295000.0 True 2 0 Stare 44 +210000.0 True 2 2 Dębiec 40 +519000.0 True 3 1 Rataje 50 +490000.0 True 4 0 Naramowice 40 +300000.0 True 2 1 Stare 23 +325000.0 True 3 4 Jeżyce 30 +238000.0 True 2 13 Rataje 49 +329000.0 True 3 1 Piątkowo 63 +270000.0 True 2 0 Piątkowo 43 +395000.0 True 3 0 Grunwald 70 +330000.0 True 2 1 Jeżyce 50 +439000.0 True 4 2 Grunwald 89 +259500.0 True 2 0 Grunwald 55 +355000.0 True 2 4 Jeżyce 56 +282000.0 True 2 1 Jeżyce 38 +335000.0 True 2 2 Górczyn 52 +375000.0 True 2 1 Grunwald 51 +399000.0 True 3 4 Stare 70 +474000.0 False 4 0 Plewiska 30 +309000.0 True 2 0 Grunwald 55 +379000.0 True 3 0 Rataje 57 +399000.0 True 3 1 Nowe 62 +570000.0 True 3 5 Grunwald 60 +105000.0 True 2 3 Nowe 50 +296000.0 True 3 6 Dębiec 63 +326000.0 True 2 1 Winiary 39 +1725000.0 True 3 0 Stare 136 +350550.0 True 3 4 Stare 50 +252000.0 True 2 12 Winogrady 47 +368000.0 True 2 2 Wilda 67 +549000.0 True 3 3 Grunwald 60 +409000.0 True 3 1 Rataje 90 +362000.0 True 2 1 Centrum 50 +250000.0 True 3 2 Nowe 80 +399900.0 True 4 2 Nowe 66 +429000.0 True 3 4 Wilda 60 +370000.0 True 2 0 Górczyn 65 +274000.0 True 2 1 Górczyn 13 +239000.0 True 2 3 Piątkowo 59 +259000.0 True 2 2 Rataje 90 +246330.0 True 2 0 Wilda 55 +289000.0 True 3 4 Winogrady 48 +100000.0 True 3 4 Stare 70 +270000.0 True 2 2 Sołacz 60 +430000.0 True 2 3 Grunwald 70 +355000.0 True 2 0 Podolany 93 +287000.0 True 2 11 Winogrady 47 +1200000.0 False 5 0 Starołęka 193 +305000.0 True 3 3 Winogrady 48 +329000.0 True 3 3 Piątkowo 60 +315000.0 True 3 0 Piątkowo 63 +267705.0 True 2 2 Grunwald 45 +247707.0 True 2 1 Jeżyce 50 +388750.0 True 4 5 Winogrady 65 +371931.0 True 4 4 Jeżyce 57 +232408.0 True 2 0 Stare 38 +247708.0 True 2 1 Jeżyce 50 +242731.0 True 2 0 Jeżyce 50 +247710.0 True 2 1 Jeżyce 50 +339200.0 True 3 1 Jeżyce 53 +349100.0 True 4 0 Rataje 85 +296277.0 True 3 1 Stare 49 +333694.0 True 3 1 Jeżyce 68 +250000.0 True 2 0 Naramowice 40 +200000.0 True 2 0 Rataje 30 +470000.0 True 4 2 Sołacz 87 +370000.0 True 4 4 Piątkowo 76 +315000.0 True 3 0 Piątkowo 60 +287000.0 True 2 10 Winogrady 80 +230000.0 True 2 3 Nowe 47 +900000.0 True 3 3 Centrum 120 +399000.0 True 3 4 Piątkowo 16 +250000.0 True 2 6 Sołacz 71 +318000.0 True 2 4 Piątkowo 20 +269000.0 True 2 9 Rataje 49 +239592.0 True 2 5 Grunwald 59 +307881.0 True 3 0 Grunwald 16 +319055.0 True 3 3 Grunwald 21 +267702.0 True 2 2 Grunwald 22 +299000.0 True 3 2 Dębiec 70 +435000.0 True 3 0 Stare 25 +690000.0 True 2 0 Grunwald 60 +204450.0 True 2 1 Nowe 33 +228144.0 True 3 2 Nowe 56 +285383.0 True 2 1 Winogrady 37 +391729.0 True 3 2 Winogrady 21 +330000.0 True 3 0 Jeżyce 78 +269984.0 True 3 4 Winogrady 76 +344141.0 True 2 8 Winogrady 47 +318384.0 True 3 6 Jeżyce 24 +249641.0 True 2 0 Jeżyce 54 +177000.0 True 2 2 Dębiec 33 +325000.0 True 2 2 Jeżyce 56 +429000.0 True 3 4 Rataje 70 +380000.0 True 3 3 Dolna 67 +448995.0 True 2 3 Jeżyce 66 +350000.0 True 2 3 Jeżyce 70 +269000.0 True 2 2 Dolna 38 +620000.0 True 3 1 Grunwald 96 +275000.0 True 2 0 Łazarz 52 +440000.0 True 2 0 Centrum 40 +505877.0 False 2 5 Centrum 22 +886860.0 False 3 5 Centrum 80 +502136.0 False 2 5 Centrum 77 +798966.0 False 2 5 Centrum 33 +561663.0 False 3 4 Centrum 69 +396248.0 False 2 4 Centrum 77 +368019.0 False 2 4 Centrum 18 +542141.0 False 3 4 Centrum 53 +698508.0 False 4 4 Centrum 59 +394787.0 False 2 4 Centrum 71 +597184.0 False 3 4 Centrum 61 +354177.0 False 2 3 Centrum 25 +353537.0 False 2 3 Centrum 17 +509468.0 False 3 3 Centrum 53 +652026.0 False 4 3 Centrum 89 +353457.0 False 2 3 Centrum 16 +356818.0 False 2 3 Centrum 58 +496573.0 False 3 2 Centrum 78 +349668.0 False 2 2 Centrum 15 +481903.0 False 3 2 Centrum 53 +309978.0 False 2 2 Centrum 16 +389528.0 False 2 2 Centrum 87 +341776.0 False 2 2 Centrum 14 +374216.0 False 2 2 Centrum 71 +534523.0 False 3 2 Centrum 62 +377418.0 False 2 1 Centrum 87 +330255.0 False 2 1 Centrum 14 +505032.0 False 3 1 Centrum 62 +375000.0 True 4 0 Grunwald 67 +375000.0 True 5 0 Grunwald 67 +363000.0 True 3 2 Grunwald 73 +495000.0 True 3 1 Grunwald 40 +270000.0 True 3 1 Starołęka 30 +365000.0 True 2 2 Grunwald 51 +450000.0 True 4 1 Grunwald 113 +190520.0 True 2 3 Nowe 30 +228492.0 True 2 1 Nowe 93 +169620.0 True 2 1 Nowe 55 +145000.0 True 2 1 Nowe 54 +270000.0 True 3 4 Rataje 48 +370000.0 True 4 4 Piątkowo 76 +289000.0 True 3 3 Grunwald 52 +585000.0 True 3 4 Jeżyce 59 +335000.0 True 3 7 Rataje 63 +329000.0 True 3 3 Piątkowo 60 +269000.0 True 2 0 Grunwald 46 +298000.0 True 2 4 Wilda 45 +398000.0 True 3 1 Grunwald 70 +395000.0 True 4 0 Grunwald 60 +389000.0 True 3 0 Wilda 96 +429000.0 True 3 4 Wilda 47 +715000.0 True 3 1 Wilda 95 +460000.0 True 2 2 Centrum 56 +555000.0 True 4 0 Stare 20 +655000.0 True 3 4 Stare 60 +188000.0 True 2 3 Stare 70 +390000.0 True 2 0 Nowe 61 +425000.0 True 2 9 Nowe 50 +359400.0 True 3 1 Stare 72 +497400.0 True 3 0 Wilda 48 +604395.0 True 5 1 Wilda 31 +330615.0 True 2 2 Stare 79 +290970.0 True 2 0 Stare 60 +283340.0 True 2 0 Stare 70 +282880.0 True 2 3 Stare 20 +339500.0 True 3 7 Nowe 80 +850000.0 True 2 7 Stare 69 +380000.0 True 4 6 Stare 90 +800000.0 True 4 3 Stare 103 +514000.0 True 4 1 Jeżyce 120 +290000.0 True 2 1 Stare 42 +640000.0 True 3 2 Stare 47 +1140000.0 True 6 0 Stare 40 +561000.0 True 2 4 Stare 50 +400000.0 True 2 1 Świerczewo 60 +220000.0 True 2 4 Grunwald 43 +490000.0 True 3 1 Jeżyce 115 +298000.0 True 2 4 Wilda 45 +449000.0 True 2 3 Jeżyce 60 +237000.0 True 2 2 Dębiec 44 +480000.0 True 2 2 Garbary 56 +298000.0 True 2 4 Wilda 37 +255000.0 True 2 3 Wilda 52 +480000.0 True 3 0 Stare 30 +451000.0 True 3 2 Wilda 30 +370000.0 True 3 4 Stare 84 +529000.0 True 3 3 Centrum 108 +360000.0 True 4 0 Grunwald 66 +419000.0 True 4 0 Kopernika 60 +350000.0 True 2 0 Stare 50 +348000.0 True 3 9 Rataje 65 +525000.0 True 4 3 Nowe 88 +450000.0 True 6 4 Wilda 90 +449000.0 True 4 2 Grunwald 90 +420000.0 True 3 0 Winogrady 58 +360000.0 True 3 3 Stare 63 +1000000.0 True 4 1 Centrum 103 +649400.0 False 3 4 Rataje 50 +311570.0 False 2 4 Rataje 51 +383928.0 False 3 3 Rataje 46 +309741.0 False 2 3 Rataje 89 +359000.0 True 2 0 Grunwald 46 +295734.0 False 2 3 Rataje 86 +384540.0 False 3 3 Rataje 55 +480000.0 True 3 1 Grunwald 40 +380091.0 False 3 2 Rataje 73 +293352.0 False 2 1 Rataje 14 +307156.0 False 2 1 Rataje 17 +293352.0 False 2 1 Rataje 14 +535000.0 True 2 3 Łazarz 59 +375606.0 False 3 1 Rataje 91 +293488.0 False 3 0 Rataje 94 +307428.0 False 2 0 Rataje 21 +293488.0 False 2 0 Rataje 16 +375408.0 False 3 0 Rataje 88 +299000.0 True 2 0 Piątkowo 47 +243828.0 False 2 4 Podolany 68 +348835.0 False 3 3 Podolany 63 +256171.0 False 2 3 Podolany 79 +298116.0 False 2 3 Podolany 96 +306247.0 False 2 3 Podolany 35 +337602.0 False 3 3 Podolany 71 +244647.0 False 2 3 Podolany 82 +641000.0 True 3 3 Łazarz 75 +277000.0 True 2 10 Nowe 80 +549000.0 True 4 0 Piątkowo 115 +499000.0 True 3 1 Suchy 95 +539000.0 True 4 2 Jeżyce 110 +450000.0 True 2 2 Grunwald 70 +242000.0 True 2 1 Grunwald 52 +310000.0 True 3 4 Jeżyce 50 +259000.0 True 2 3 Winogrady 40 +475000.0 True 3 4 Wilda 66 +120000.0 True 3 3 Grunwald 35 +270000.0 True 3 4 Rataje 48 +1850000.0 True 5 1 Grunwald 196 +350000.0 True 4 4 Grunwald 50 +280000.0 True 4 4 Grunwald 40 +490000.0 True 4 4 Grunwald 70 +495000.0 True 3 1 Naramowice 70 +545000.0 True 3 0 Rataje 71 +310000.0 True 3 10 Rataje 80 +215000.0 True 2 0 Wilda 36 +295000.0 True 2 4 Garbary 33 +200000.0 True 2 8 Dębiec 50 +359900.0 True 4 4 Rataje 74 +320000.0 True 3 3 Jeżyce 70 +300000.0 True 2 1 Naramowice 23 +535000.0 True 4 2 Wilda 120 +620000.0 True 3 2 Naramowice 60 +597000.0 True 3 0 Naramowice 60 +399000.0 True 3 0 Winogrady 62 +390000.0 True 3 0 Grunwald 75 +310000.0 True 2 1 Rataje 30 +365000.0 True 3 1 Rataje 88 +382000.0 True 3 3 Centrum 30 +299000.0 True 2 2 Sołacz 58 +299000.0 True 2 2 Sołacz 58 +499000.0 True 3 1 Grunwald 64 +549000.0 True 3 2 Jeżyce 106 +549000.0 True 3 2 Jeżyce 106 +413000.0 True 3 3 Łazarz 46 +259000.0 True 2 1 Jeżyce 47 +949000.0 True 3 4 Śródka 98 +949000.0 True 3 4 Śródka 98 +270000.0 True 3 4 Rataje 48 +348000.0 True 3 9 Nowe 65 +260000.0 True 2 0 Ławica 60 +370000.0 True 4 4 Stare 60 +399000.0 True 3 4 Stare 16 +369000.0 True 4 3 Grunwald 74 +224000.0 True 2 0 Łazarz 50 +260000.0 True 3 4 Grunwald 49 +315000.0 True 3 0 Piątkowo 60 +379999.0 True 3 3 Wilda 67 +350000.0 True 2 1 Rataje 63 +270000.0 True 2 4 Grunwald 38 +439000.0 True 4 2 Łazarz 92 +519000.0 True 3 1 Rataje 50 +290000.0 True 2 2 Dębiec 66 +326000.0 True 2 4 Łazarz 80 +240000.0 True 2 3 Grunwald 42 +389000.0 True 3 0 Wilda 67 +420000.0 True 3 2 Dębiec 91 +279000.0 True 2 1 Naramowice 51 +220000.0 True 2 4 Grunwald 43 +465360.0 True 2 2 Grunwald 17 +777280.0 True 3 3 Grunwald 16 +1000000.0 True 4 1 Stare 146 +350000.0 True 2 3 Rataje 50 +469000.0 True 4 2 Jeżyce 87 +253498.0 True 2 5 Jeżyce 38 +334752.0 True 3 3 Jeżyce 51 +374792.0 True 4 5 Jeżyce 57 +329000.0 True 3 4 Rataje 63 +349668.0 False 2 2 Stare 15 +297420.0 False 2 3 Grunwald 24 +297420.0 False 2 3 Grunwald 24 +220000.0 True 2 1 Jeżyce 60 +399000.0 True 3 1 Sołacz 66 +488000.0 True 3 3 Grunwald 70 +220000.0 True 2 4 Grunwald 43 +390000.0 True 3 2 Podolany 68 +299000.0 True 2 0 Wilda 52 +234000.0 True 2 0 Wilda 37 +375000.0 True 3 2 Wilda 90 +820000.0 True 4 0 Centrum 163 +320000.0 True 3 4 Winogrady 50 +420000.0 False 4 0 Grunwald 82 +495000.0 True 4 1 Stare 98 +279000.0 True 2 1 Stare 52 +620000.0 True 3 1 Stare 99 +329000.0 True 2 1 Stare 54 +699000.0 True 3 2 Stare 92 +487000.0 True 3 0 Stare 73 +375000.0 True 3 0 Naramowice 69 +269000.0 True 2 9 Rataje 49 +220000.0 True 2 4 Grunwald 43 +230000.0 True 2 1 Dębiec 38 +435000.0 True 2 0 Górczyn 60 +390000.0 True 3 2 Podolany 68 +446240.0 True 2 1 Grunwald 78 +390000.0 True 3 2 Podolany 68 +619000.0 True 3 2 Winogrady 100 +240000.0 True 2 3 Dębiec 50 +270000.0 True 3 4 Rataje 48 +244968.0 True 2 0 Stare 42 +285679.0 True 2 4 Winogrady 48 +260000.0 True 2 6 Winiary 70 +585000.0 True 4 1 Piątkowo 100 +329000.0 True 3 1 Piątkowo 63 +269000.0 True 2 0 Naramowice 46 +348000.0 True 3 9 Rataje 65 +270000.0 True 3 4 Rataje 48 +359605.0 True 3 5 Grunwald 58 +375529.0 False 2 3 Stare 71 +247705.0 False 2 1 Podolany 74 +247705.0 False 2 1 Piątkowo 74 +156085.0 False 2 4 Głuszyna 45 +411684.0 False 3 3 Winogrady 17 +349000.0 False 4 0 Szczepankowo 29 +277823.0 False 2 2 Podolany 70 +249733.0 False 2 0 Ogrody 54 +424377.0 False 4 2 Starołęka 14 +282944.0 False 2 0 Starołęka 59 +460499.0 False 3 1 Stare 51 +270000.0 True 3 0 Grunwald 48 +350000.0 True 4 1 Wilda 80 +350000.0 True 4 4 Winogrady 90 +323000.0 True 4 0 Winogrady 56 +649000.0 True 4 4 Centrum 109 +341704.0 True 3 8 Grunwald 56 +297421.0 True 2 3 Grunwald 50 +245832.0 True 2 2 Grunwald 40 +285384.0 True 2 4 Winogrady 48 +240000.0 True 2 1 Wilda 40 +345865.0 True 3 2 Jeżyce 21 +261000.0 True 2 2 Jeżyce 57 +400000.0 True 3 2 Jeżyce 74 +400000.0 True 2 2 Jeżyce 74 +348000.0 True 3 9 Rataje 65 +369000.0 True 2 2 Grunwald 51 +339000.0 True 3 0 Rataje 63 +250000.0 True 2 4 Rataje 23 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3 Piątkowo 60 +260000.0 True 3 0 Jeżyce 74 +266000.0 True 2 2 Piątkowo 49 +316498.0 True 2 2 Stare 77 +519000.0 True 3 1 Rataje 50 +442150.0 True 2 2 Stare 75 +395000.0 True 3 2 Centrum 74 +599000.0 True 2 1 Centrum 70 +459000.0 True 2 1 Centrum 48 +339000.0 True 3 1 Winogrady 51 +375000.0 True 3 2 Jeżyce 50 +289000.0 True 2 4 Ogrody 41 +230000.0 True 2 5 Winogrady 60 +440000.0 True 2 4 Centrum 55 +599000.0 True 3 2 Centrum 80 +343200.0 True 3 4 Winogrady 52 +385000.0 True 2 1 Centrum 60 +300000.0 True 3 3 Centrum 88 +529000.0 True 4 4 Centrum 85 +349000.0 True 3 3 Wilda 82 +405000.0 True 4 2 Nowe 71 +355000.0 True 2 4 Jeżyce 89 +235000.0 True 2 0 Górczyn 50 +495000.0 True 4 1 Grunwald 64 +285000.0 True 2 3 Wilda 60 +385000.0 True 3 4 Łazarz 82 +379999.0 True 3 3 Wilda 67 +370000.0 True 2 13 Rataje 67 +450000.0 True 3 0 Naramowice 71 +479000.0 True 3 3 Górczyn 70 +439000.0 True 4 2 Łazarz 40 +385000.0 True 3 0 Łazarz 80 +550000.0 True 4 1 Łazarz 50 +260000.0 True 3 4 Grunwald 47 +755000.0 True 4 2 Łazarz 90 +319000.0 True 2 0 Górczyn 54 +380000.0 True 3 1 Łazarz 30 +530000.0 True 3 1 Piątkowo 76 +900000.0 True 3 2 Grunwald 112 +375000.0 True 3 8 Piątkowo 75 +576500.0 True 2 5 Centrum 50 +576500.0 True 2 5 Chwaliszewo 50 +438503.0 True 3 2 Centrum 57 +354454.0 False 2 3 Grunwald 17 +489780.0 False 4 2 Górczyn 63 +491520.0 False 4 1 Górczyn 92 +273875.5 False 2 1 Grunwald 13 +267000.0 True 2 2 Dębiec 35 +260000.0 True 2 2 Piątkowo 90 +587000.0 True 4 3 Łazarz 38 +460000.0 True 3 1 Naramowice 110 +695000.0 True 4 1 Rataje 70 +506657.0 True 4 11 Grunwald 73 +298250.0 True 2 5 Grunwald 38 +297421.0 True 2 2 Grunwald 24 +275000.0 True 2 9 Nowe 38 +267000.0 True 2 4 Nowe 70 +447000.0 True 3 4 Grunwald 20 +349900.0 True 3 4 Wilda 42 +360000.0 True 4 0 Centrum 66 +525000.0 True 4 3 Jeżyce 70 +450000.0 True 3 2 Strzeszyn 70 +690000.0 True 4 5 Górczyn 25 +334000.0 True 2 4 Sołacz 50 +240000.0 True 2 3 Jeżyce 43 +307000.0 True 3 2 Rataje 48 +307000.0 True 2 2 Rataje 48 +345000.0 True 3 8 Nowe 63 +333694.0 False 3 1 Podolany 32 +333694.0 False 3 1 Piątkowo 38 +299000.0 True 3 0 Grunwald 53 +389000.0 True 3 3 Stare 49 +310000.0 True 2 2 Centrum 74 +220000.0 True 2 0 Grunwald 50 +332800.0 True 2 1 Grunwald 52 +240000.0 True 2 2 Stare 38 +323206.0 False 2 2 Naramowice 50 +558745.0 False 3 3 Stare 62 +290000.0 True 2 6 Jeżyce 49 +285000.0 True 2 3 Piątkowo 49 +365000.0 True 3 1 Rataje 67 +263000.0 True 2 1 Rataje 47 +289000.0 True 2 2 Jeżyce 42 +265000.0 True 3 4 Grunwald 48 +310000.0 True 2 1 Nowe 40 +300000.0 True 3 2 Winogrady 48 +565964.0 True 2 5 Centrum 49 +747000.0 True 3 7 Rataje 84 +275000.0 True 2 0 Naramowice 50 +405000.0 True 4 2 Rataje 71 +491520.0 True 4 1 Górczyn 92 +363258.0 True 2 1 Górczyn 59 +305739.0 True 2 2 Górczyn 53 +399000.0 True 3 4 Piątkowo 69 +280000.0 True 2 1 Sołacz 38 +299900.0 True 2 0 Dębiec 48 +420000.0 True 2 3 Naramowice 59 +650000.0 True 4 8 Rataje 100 +329000.0 True 3 3 Wilda 82 +355000.0 True 3 2 Piątkowo 66 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Centrum 161 +379000.0 True 2 0 Nowe 56 +560000.0 True 2 8 Grunwald 55 +335400.0 True 2 1 Łazarz 51 +290000.0 True 2 5 Winogrady 42 +235000.0 True 2 3 Winogrady 38 +300000.0 True 2 4 Winogrady 53 +399000.0 True 3 1 Winiary 66 +830000.0 True 3 1 Grunwald 91 +385500.0 True 2 6 Dębiec 38 +199000.0 True 5 0 Sołacz 129 +295000.0 True 2 4 Stare 33 +370000.0 True 4 11 Rataje 74 +335000.0 True 3 1 Piątkowo 63 +350000.0 True 3 7 Piątkowo 63 +380000.0 True 3 1 Łazarz 98 +184000.0 True 2 0 Grunwald 34 +855000.0 True 4 5 Jeżyce 96 +215000.0 True 2 0 Wilda 36 +495000.0 True 4 1 Naramowice 98 +250000.0 True 2 5 Nowe 50 +275000.0 True 3 7 Wilda 53 +409000.0 True 3 1 Malta 61 +200000.0 True 2 0 Głuszyna 52 +299000.0 True 3 3 Wilda 66 +490000.0 True 4 3 Sołacz 83 +245000.0 True 2 0 Stare 44 +950000.0 True 3 4 Nowe 99 +355000.0 True 2 3 Nowe 50 +380000.0 True 3 3 Łazarz 95 +525000.0 True 4 3 Jeżyce 104 +400000.0 True 2 3 Naramowice 50 +248000.0 True 2 10 Grunwald 42 +380000.0 True 3 0 Centrum 55 +453600.0 True 2 3 Naramowice 56 +290000.0 True 2 3 Winogrady 37 +690000.0 True 4 5 Grunwald 107 +350000.0 True 3 6 Jeżyce 64 +340000.0 True 4 3 Winogrady 65 +345000.0 True 3 1 Rataje 78 +395000.0 True 3 10 Piątkowo 67 +495000.0 True 5 1 Naramowice 98 +269000.0 True 2 3 Grunwald 47 +257000.0 True 2 12 Winogrady 46 +516000.0 True 3 3 Naramowice 75 +285000.0 True 2 4 Naramowice 42 +354000.0 True 3 1 Naramowice 60 +345000.0 True 2 0 Centrum 42 +550000.0 True 2 1 Naramowice 57 +670000.0 True 4 3 Grunwald 81 +659000.0 True 5 0 Podolany 135 +925000.0 True 5 1 Stare 105 +510000.0 True 5 1 Naramowice 98 +350000.0 True 3 3 Jeżyce 70 +345000.0 True 3 1 Winogrady 50 +279000.0 True 2 0 Piątkowo 48 +535000.0 True 2 2 Stare 55 +350000.0 True 2 1 Rataje 54 +349000.0 True 3 3 Rataje 63 +250000.0 True 2 3 Wilda 39 +270000.0 True 2 10 Nowe 48 +285000.0 True 2 0 Łazarz 49 +999000.0 True 3 4 Nowe 99 +425000.0 True 3 1 Piątkowo 74 +479000.0 True 3 1 Naramowice 66 +360000.0 True 3 0 Wilda 112 +495000.0 True 3 1 Łazarz 64 +599000.0 True 3 3 Grunwald 60 +390000.0 True 3 2 Podolany 68 +450000.0 True 4 1 Grunwald 101 +313000.0 True 2 4 Piątkowo 49 +338000.0 True 3 3 Wilda 63 +285000.0 True 2 11 Winogrady 47 +270000.0 True 2 0 Grunwald 42 +360000.0 True 4 4 Jeżyce 60 +399000.0 True 2 3 Centrum 60 +619000.0 True 3 5 Jeżyce 69 +330000.0 True 2 1 Jeżyce 53 +1612000.0 True 7 5 Jeżyce 166 +399000.0 True 3 3 Centrum 50 +365000.0 True 2 1 Stare 50 +450000.0 True 3 0 Grunwald 75 +288000.0 True 3 4 Winogrady 47 +240000.0 True 2 16 Rataje 36 +326000.0 True 2 0 Jeżyce 55 +250000.0 True 2 4 Zawady 66 +288000.0 True 2 4 Naramowice 44 +289000.0 True 2 7 Winiary 49 +515000.0 True 3 0 Rataje 69 +428000.0 True 3 3 Centrum 43 +510000.0 True 5 1 Naramowice 98 +320000.0 True 2 2 Piątkowo 48 +659200.0 True 4 3 Łazarz 103 +499000.0 True 5 0 Grunwald 130 +240000.0 True 2 2 Dębiec 48 +495000.0 True 4 1 Naramowice 98 +320000.0 True 3 0 Rataje 56 +430000.0 True 3 2 Rataje 64 +409000.0 True 5 4 Winogrady 64 +415000.0 True 3 4 Łazarz 53 +359000.0 True 3 2 Rataje 65 +410000.0 True 2 5 Rataje 53 +479000.0 True 3 3 Nowe 83 +365000.0 True 4 3 Grunwald 68 +369000.0 True 2 3 Grunwald 64 +259000.0 True 2 2 Nowe 42 +250000.0 True 3 4 Dębiec 45 +299000.0 True 2 4 Nowe 47 +430000.0 True 2 1 Centrum 72 +275000.0 True 2 0 Dębiec 50 +950000.0 True 3 4 Nowe 99 +329000.0 True 3 7 Rataje 78 +380000.0 True 4 6 Piątkowo 73 +299000.0 True 2 5 Centrum 49 +265000.0 True 2 1 Wilda 44 +370000.0 True 2 13 Rataje 48 +370000.0 True 4 4 Piątkowo 76 +379000.0 True 3 1 Piątkowo 78 +299000.0 True 2 3 Grunwald 44 +379999.0 True 2 5 Jeżyce 61 +1000000.0 True 5 1 Jeżyce 128 +549000.0 True 3 2 Jeżyce 106 +335000.0 True 3 9 Nowe 65 +489000.0 True 3 0 Jeżyce 65 +379000.0 True 3 4 Rataje 63 +245000.0 True 3 0 Grunwald 45 +235000.0 True 2 0 Łazarz 52 +295555.0 True 2 1 Jeżyce 45 +224000.0 True 2 0 Górczyn 38 +315000.0 True 2 2 Winogrady 38 +429000.0 True 3 4 Nowe 79 +595000.0 True 3 0 Naramowice 94 +330000.0 True 3 0 Bonin 56 +275000.0 True 2 13 Rataje 49 +499000.0 True 4 2 Wilda 120 +287000.0 True 2 10 Winogrady 46 +280000.0 True 2 10 Piątkowo 46 +273875.0 True 2 1 Górczyn 13 +450000.0 True 3 0 Winogrady 70 +325000.0 True 3 4 Jeżyce 64 +299817.0 True 2 3 Górczyn 59 +295000.0 True 2 2 Naramowice 58 +380000.0 True 4 6 Piątkowo 73 +399000.0 True 3 4 Winogrady 65 +305000.0 True 3 3 Winogrady 48 +220000.0 True 2 3 Jeżyce 37 +285000.0 True 3 2 Antoninek 61 +238000.0 True 2 2 Grunwald 37 +200000.0 True 2 0 Rataje 30 +298000.0 True 2 5 Centrum 50 +391729.0 False 3 2 Winogrady 42 +347090.0 False 3 2 Winogrady 41 +285678.0 False 2 1 Winogrady 82 +321656.0 False 2 4 Winogrady 38 +312259.0 False 2 6 Winogrady 60 +347090.0 False 3 1 Winogrady 90 +355042.0 False 3 6 Jeżyce 96 +496573.0 False 3 2 Stare 78 +300680.0 False 2 2 Starołęka 54 +395000.0 True 4 4 Piątkowo 90 +771672.0 False 4 4 Górczyn 66 +399000.0 True 4 1 Szczepankowo 60 +340100.0 True 3 0 Szczepankowo 45 +225228.0 False 2 5 Rataje 91 +324387.0 False 2 9 Grunwald 49 +362459.0 False 3 0 Starołęka 80 +247705.0 False 2 1 Podolany 74 +339000.0 True 3 8 Nowe 78 +207000.0 True 2 2 Wilda 33 +295000.0 True 2 4 Grunwald 50 +324500.0 True 2 5 Wilda 65 +429000.0 True 3 4 Wilda 47 +399000.0 True 4 0 Szczepankowo 71 +411804.0 True 3 1 Winogrady 42 +282613.0 True 2 3 Winogrady 33 +235399.0 True 2 1 Winogrady 59 +265741.0 True 2 7 Winogrady 21 +323340.0 True 3 3 Winogrady 89 +293848.0 True 3 7 Winogrady 57 +337303.0 True 4 2 Winogrady 17 +470092.0 True 2 3 Centrum 21 +310000.0 True 2 0 Wilda 53 +365000.0 True 4 1 Nowe 54 +259000.0 True 2 6 Winogrady 38 +414225.0 True 3 3 Centrum 23 +489000.0 True 3 3 Grunwald 104 +350000.0 True 4 3 Grunwald 30 +325000.0 True 2 3 Rataje 20 +321845.0 False 3 1 Grunwald 55 +248000.0 True 2 14 Rataje 49 +286000.0 True 2 5 Centrum 64 +399000.0 True 3 4 Piątkowo 16 +289000.0 True 2 7 Winiary 80 +329000.0 True 3 11 Winogrady 50 +252723.0 False 2 1 Winogrady 43 +300680.0 False 2 2 Starołęka 54 +496573.0 False 3 2 Stare 78 +392181.0 False 3 4 Winogrady 42 +496573.0 False 3 2 Stare 78 +412438.0 False 3 2 Naramowice 17 +286000.0 True 2 5 Centrum 49 +269000.0 True 2 9 Rataje 49 +315000.0 True 2 1 Grunwald 61 +318390.0 True 3 3 Jeżyce 48 +242406.0 True 2 0 Jeżyce 36 +296278.0 True 3 2 Stare 49 +223747.0 True 2 0 Stare 37 +388755.0 True 4 5 Winogrady 65 +347095.0 True 3 1 Winogrady 57 +269000.0 True 2 1 Ogrody 50 +285000.0 True 2 9 Grunwald 50 +114642.0 True 2 0 Łazarz 46 +286000.0 True 2 5 Stare 64 +333693.0 True 3 1 Jeżyce 68 +435000.0 True 2 0 Świerczewo 60 +320000.0 True 4 1 Jeżyce 40 +395000.0 True 4 0 Grunwald 60 +353457.0 True 2 3 Stare 44 +267704.0 True 2 3 Grunwald 45 +245831.0 True 2 2 Grunwald 40 +391729.0 True 3 2 Winogrady 69 +240875.0 True 2 7 Stare 39 +424380.0 True 4 2 Nowe 74 +282996.0 True 2 0 Nowe 55 +285000.0 True 3 1 Rataje 48 +284618.0 False 2 3 Nowe 55 +512034.0 False 4 2 Winogrady 94 +284618.0 False 2 3 Nowe 55 +255404.0 False 2 6 Jeżyce 12 +315810.0 False 3 8 Winogrady 20 +282994.0 False 2 0 Starołęka 59 +637135.0 False 3 7 Grunwald 65 +754000.0 False 5 0 Morasko 42 +336000.0 True 3 0 Szczepankowo 85 +355000.0 True 2 3 Nowe 90 +475000.0 True 3 0 Rataje 73 +275000.0 True 3 4 Winogrady 60 +275000.0 True 3 4 Winogrady 70 +289000.0 True 2 7 Winogrady 80 +315000.0 True 3 0 Rataje 63 +260000.0 True 2 1 Łazarz 54 +370000.0 True 4 4 Piątkowo 76 +319990.0 True 2 3 Jeżyce 70 +156085.0 False 2 3 Głuszyna 45 +225228.0 False 2 5 Rataje 91 +308237.0 False 2 1 Nowe 85 +353275.0 False 2 14 Grunwald 74 +228144.0 False 3 2 Głuszyna 56 +156085.0 False 2 2 Głuszyna 45 +353275.0 False 2 14 Grunwald 74 +353275.0 False 2 14 Grunwald 74 +156085.0 False 2 3 Głuszyna 45 +156085.0 False 2 4 Nowe 54 +267702.0 False 2 3 Grunwald 22 +353275.0 False 2 14 Grunwald 74 +247705.0 False 2 1 Podolany 74 +315810.0 False 3 8 Winogrady 20 +370000.0 True 4 4 Stare 60 +265000.0 True 2 2 Stare 70 +304140.0 False 3 3 Winogrady 27 +394000.0 False 4 0 Szczepankowo 77 +287882.0 False 2 1 Starołęka 85 +729000.0 True 3 0 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45 +356251.0 True 3 14 Grunwald 57 +225290.0 True 2 7 Rataje 39 +333701.0 True 3 1 Jeżyce 68 +368568.0 True 3 4 Jeżyce 68 +285000.0 True 3 2 Antoninek 61 +300000.0 True 2 9 Strzeszyn 45 +299000.0 True 2 5 Centrum 50 +249000.0 True 2 2 Grunwald 46 +599000.0 True 4 5 Malta 84 +250000.0 True 2 4 Wilda 54 +341776.0 True 2 2 Stare 44 +238000.0 True 2 13 Rataje 49 +279000.0 True 3 1 Wilda 68 +430000.0 True 2 3 Jeżyce 58 +255000.0 True 2 1 Winogrady 38 +360000.0 True 3 1 Grunwald 49 +339000.0 True 2 1 Górczyn 45 +855000.0 True 3 3 Centrum 90 +1179000.0 True 3 2 Centrum 40 +2700000.0 True 3 2 Centrum 90 +1170000.0 True 3 3 Centrum 90 +368712.0 True 2 2 Centrum 90 +991380.0 True 4 1 Nowe 20 +250000.0 True 2 3 Dębiec 53 +249000.0 True 3 4 Rataje 53 +350000.0 True 2 4 Jeżyce 56 +285000.0 True 2 2 Centrum 52 +285000.0 True 2 2 Łazarz 52 +490000.0 True 4 2 Jeżyce 87 +429000.0 True 4 2 Grunwald 92 +211190.0 False 2 0 Podolany 78 +375529.0 False 2 3 Centrum 71 +225228.0 False 2 0 Rataje 71 +991380.0 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True 2 4 Jeżyce 25 +240158.0 True 2 0 Stare 39 +211190.0 True 2 0 Jeżyce 38 +333690.0 True 3 2 Jeżyce 68 +388751.0 True 4 5 Winogrady 65 +347091.0 True 3 1 Winogrady 57 +362450.0 True 3 1 Górczyn 90 +225288.91 True 2 6 Rataje 91 +225288.91 True 2 5 Rataje 91 +225288.91 True 2 1 Rataje 91 +392860.63 True 4 3 Winogrady 41 +364762.0 True 4 4 Winogrady 89 +316498.0 True 2 2 Centrum 77 +442002.0 True 2 3 Centrum 73 +276610.0 True 2 4 Centrum 80 +316355.0 True 2 4 Centrum 67 +280250.0 True 2 0 Górczyn 50 +327127.5 True 2 0 Centrum 50 +449000.0 False 5 0 Szczepankowo 68 +225288.0 False 2 1 Rataje 91 +286327.0 False 2 3 Naramowice 82 +365690.0 False 4 2 Naramowice 50 +389528.0 False 2 2 Stare 87 +481903.0 False 3 2 Stare 53 +349000.0 False 4 0 Szczepankowo 29 +347090.0 False 3 2 Naramowice 41 +534523.0 False 3 2 Stare 62 +412670.0 False 3 1 Naramowice 17 +285678.0 False 2 2 Naramowice 82 +263000.0 True 2 0 Wilda 75 +245000.0 True 2 2 Winogrady 20 +232410.0 True 2 0 Stare 38 +245488.0 True 2 0 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False 2 0 Winogrady 79 +349000.0 False 4 0 Szczepankowo 29 +277823.0 False 2 2 Podolany 70 +310020.0 False 3 4 Winogrady 67 +249733.0 False 2 0 Ogrody 54 +424377.0 False 4 2 Starołęka 14 +282944.0 False 2 0 Starołęka 59 +282944.0 False 2 0 Starołęka 59 +347633.0 True 3 10 Grunwald 57 +293436.0 True 2 1 Grunwald 50 +247705.0 True 2 1 Jeżyce 50 +398000.0 True 3 1 Jeżyce 72 +570000.0 True 4 0 Jeżyce 90 +285200.0 True 2 1 Stare 46 +347100.0 True 3 1 Winogrady 57 +223749.0 True 2 0 Stare 37 +245880.0 True 2 1 Jeżyce 38 +460050.0 True 3 5 Grunwald 74 +329000.0 True 3 2 Piątkowo 40 +279000.0 True 2 1 Stare 60 +720000.0 True 4 7 Jeżyce 90 +225290.0 True 2 5 Rataje 39 +355000.0 False 3 0 Stare 61 +355000.0 False 3 0 Podolany 61 +430000.0 False 4 0 Podolany 75 +270000.0 True 3 3 Stare 47 +475000.0 False 4 0 Stare 72 +475000.0 False 4 0 Podolany 72 +325000.0 True 2 2 Centrum 51 +455000.0 False 4 0 Stare 72 +455000.0 False 4 0 Podolany 72 +372000.0 False 4 1 Grunwald 87 +270000.0 True 2 10 Śródka 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+299000.0 True 2 0 Grunwald 51 +339000.0 True 2 2 Centrum 53 +320000.0 True 3 4 Stare 65 +364000.0 True 3 1 Nowe 67 +209000.0 True 3 3 Grunwald 50 diff --git a/w2/data_flats_with_outliers.tsv b/w2/data_flats_with_outliers.tsv new file mode 100644 index 0000000..607342a --- /dev/null +++ b/w2/data_flats_with_outliers.tsv @@ -0,0 +1,4186 @@ +476118.0 False 3 1 Centrum 78 +349000.0 False 5 0 4 103 +390000.0 False 4 1 Naramowice 100 +530000.0 True 4 3 Jeżyce 70 +364000.0 False 5 0 4 126 +294000.0 False 2 0 Grunwald 46 +277806.0 False 2 1 Dolna 47 +571229.15 False 2 4 Wilda 39 +346777.0 False 3 1 Grunwald 10 +279924.0 False 2 2 Dolna 2 +304000.0 False 2 1 Wilda 95 +604836.0 False 4 5 Grunwald 40 +268229.0 False 2 1 Grunwald 90 +325000.0 False 3 1 Grunwald 54 +274200.0 False 2 0 Grunwald 57 +333694.0 False 3 0 Podolany 38 +249964.0 False 3 0 Nowe 41 +833018.0 False 5 5 Dolna 31 +399406.0 False 3 2 Wilda 89 +277823.0 False 2 4 Podolany 70 +427202.0 False 3 3 Dolna 79 +242751.0 False 2 1 Wilda 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53 +300000.0 True 2 4 Winogrady 53 +335400.0 True 2 1 Łazarz 51 +560000.0 True 2 8 Grunwald 55 +855000.0 True 4 5 Jeżyce 96 +399000.0 True 3 1 Winiary 66 +750000.0 True 4 0 Kobylepole 105 +459000.0 True 3 4 Dębiec 60 +275000.0 True 2 0 Naramowice 50 +925000.0 True 5 1 Stare 105 +350000.0 True 3 3 Jeżyce 70 +550000.0 True 2 1 Naramowice 57 +345000.0 True 2 0 Centrum 42 +576520.0 True 2 5 Centrum 50 +285000.0 True 2 4 Naramowice 42 +395000.0 True 3 10 Piątkowo 67 +516000.0 True 3 3 Naramowice 75 +620000.0 True 3 2 Naramowice 98 +240000.0 True 2 3 Grunwald 38 +350000.0 True 2 0 Naramowice 48 +390000.0 True 3 2 Podolany 68 +339000.0 True 3 9 Rataje 65 +659000.0 True 5 0 Podolany 135 +670000.0 True 4 3 Grunwald 81 +390000.0 True 3 2 Podolany 68 +420000.0 True 2 1 Naramowice 62 +288000.0 True 3 4 Winogrady 47 +326000.0 True 2 0 Jeżyce 55 +450000.0 True 3 0 Grunwald 75 +354000.0 True 3 1 Naramowice 60 +279000.0 True 2 0 Piątkowo 48 +449900.0 True 3 0 Naramowice 71 +285000.0 True 2 11 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3 9 Rataje 65 +340000.0 True 3 8 Rataje 65 +325248.0 True 3 1 Jeżyce 49 +262875.0 True 2 4 Jeżyce 40 +325248.0 True 3 1 Jeżyce 49 +262874.0 True 2 4 Jeżyce 40 +253498.0 True 2 4 Jeżyce 38 +253193.0 True 2 6 Jeżyce 38 +253193.0 True 2 4 Jeżyce 38 +220000.0 True 2 1 Łazarz 45 +230000.0 True 2 2 Rataje 49 +293848.0 True 3 4 Winogrady 49 +305000.0 True 3 4 Jeżyce 84 +245000.0 True 2 2 Jeżyce 62 +205000.0 True 2 0 Jeżyce 43 +269000.0 True 2 13 Piątkowo 50 +249000.0 True 2 2 Strzeszyn 34 +330000.0 True 3 6 Rataje 80 +200000.0 True 2 0 Wilda 32 +270000.0 True 3 4 Rataje 48 +617360.0 True 3 3 Grunwald 77 +279554.0 True 2 4 Jeżyce 68 +279554.0 True 2 4 Jeżyce 68 +550000.0 True 3 1 Grunwald 73 +355000.0 True 2 8 Ogrody 52 +210000.0 True 2 10 Ogrody 38 +234000.0 True 2 0 Wilda 37 +375000.0 True 3 2 Wilda 90 +345000.0 True 3 6 Winogrady 10 +320000.0 True 3 4 Piątkowo 63 +239000.0 True 2 8 Winogrady 38 +350000.0 True 4 4 Piątkowo 74 +295363.0 True 3 1 Stare 48 +285384.0 True 2 4 Winogrady 48 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Dębiec 35 +260000.0 True 2 2 Piątkowo 90 +587000.0 True 4 3 Łazarz 38 +460000.0 True 3 1 Naramowice 110 +695000.0 True 4 1 Rataje 70 +506657.0 True 4 11 Grunwald 73 +338325.0 True 2 13 Grunwald 5 +249641.0 True 2 0 Ogrody 54 +298250.0 True 2 5 Grunwald 38 +297421.0 True 2 2 Grunwald 24 +275000.0 True 2 9 Nowe 38 +249641.0 True 2 0 Jeżyce 54 +344141.0 True 2 8 Winogrady 47 +318384.0 True 3 6 Jeżyce 24 +269984.0 True 3 4 Winogrady 76 +447000.0 True 3 4 Grunwald 20 +450000.0 True 3 2 Strzeszyn 70 +690000.0 True 4 5 Górczyn 25 +334000.0 True 2 4 Sołacz 50 +289476.0 False 2 3 Jeżyce 84 +533745.0 False 5 2 Starołęka 4 +333694.0 False 3 1 Podolany 32 +333694.0 False 3 1 Piątkowo 38 +310000.0 True 2 2 Centrum 74 +310000.0 True 2 1 Grunwald 52 +250000.0 True 2 2 Łazarz 36 +265000.0 True 2 4 Jeżyce 43 +558745.0 False 3 3 Stare 62 +298000.0 True 2 5 Centrum 50 +347090.0 False 3 1 Winogrady 90 +362459.0 False 3 0 Starołęka 80 +754000.0 True 7 1 Stare 116 +247705.0 False 2 1 Podolany 74 +313000.0 True 2 4 Piątkowo 49 +339000.0 True 3 8 Nowe 78 +207000.0 True 2 2 Wilda 33 +295000.0 True 2 4 Grunwald 50 +330000.0 True 3 0 Jeżyce 78 +324500.0 True 2 5 Wilda 65 +429000.0 True 3 4 Wilda 47 +275000.0 True 2 9 Rataje 38 +365000.0 True 4 1 Nowe 54 +259000.0 True 2 6 Winogrady 38 +369000.0 True 2 3 Piątkowo 60 +414225.0 True 3 3 Centrum 23 +269000.0 True 3 3 Winogrady 48 +320000.0 True 2 3 Rataje 20 +288465.0 True 2 1 Starołęka 77 +321845.0 False 3 1 Grunwald 55 +389000.0 True 3 4 Piątkowo 16 +289000.0 True 2 7 Winiary 80 +249000.0 True 2 0 Komorniki 53 +391729.0 True 3 2 Winogrady 21 +285383.0 True 2 1 Winogrady 37 +228144.0 True 3 2 Nowe 56 +204450.0 True 2 1 Nowe 33 +496573.0 False 3 2 Stare 78 +286000.0 True 2 5 Centrum 49 +269000.0 True 2 1 Ogrody 50 +114642.0 True 2 0 Łazarz 46 +286000.0 True 2 5 Centrum 49 +390000.0 True 2 0 Świerczewo 60 +320000.0 True 4 1 Jeżyce 40 +706655.0 False 3 2 Nowe 45 +754000.0 False 5 0 Morasko 42 +259000.0 True 3 4 Winogrady 60 +289000.0 True 2 7 Winogrady 80 +350000.0 True 3 0 Rataje 63 +260000.0 True 2 1 Łazarz 54 +319990.0 True 2 3 Jeżyce 70 +228144.0 False 3 2 Głuszyna 56 +156085.0 False 2 2 Głuszyna 45 +350000.0 True 4 4 Stare 60 +394000.0 False 4 0 Szczepankowo 77 +287882.0 False 2 1 Starołęka 85 +445000.0 True 4 3 Piątkowo 65 +229000.0 True 2 1 Grunwald 16 +220000.0 True 2 3 Jeżyce 37 +285000.0 True 3 2 Antoninek 61 +550000.0 True 3 1 Jeżyce 73 +504326.0 True 4 4 Stare 26 +371930.0 True 4 2 Jeżyce 57 +255000.0 True 3 2 Grunwald 20 +279000.0 True 2 3 Piątkowo 30 +325000.0 True 2 0 Nowe 80 +604395.0 True 5 1 Wilda 31 +558000.0 True 5 1 Wilda 2 +1007500.0 False 4 1 Starołęka 94 +1203616.0 False 5 0 Starołęka 71 +298980.0 False 2 5 Winogrady 30 +263140.0 False 2 0 Naramowice 5 +281988.0 False 2 7 Naramowice 76 +349000.0 False 4 0 Szczepankowo 29 +277823.0 False 2 2 Podolany 70 +424377.0 False 4 2 Starołęka 14 +282944.0 False 2 0 Starołęka 59 +282944.0 False 2 0 Starołęka 59 +349668.0 False 2 2 Stare 15 +321904.0 False 2 4 Winogrady 92 +367000.0 True 3 1 Centrum 30 +350000.0 True 3 1 Nowe 63 +350000.0 True 2 1 Rataje 63 +399000.0 True 3 5 Grunwald 98 +429000.0 True 3 3 Centrum 102 +451000.0 True 3 2 Wilda 30 +565000.0 True 4 0 Sołacz 90 +285000.0 True 3 2 Antoninek 61 +350000.0 True 2 1 Rataje 54 +299000.0 True 2 5 Centrum 50 +269000.0 True 2 9 Rataje 49 +249000.0 True 2 2 Grunwald 46 +285000.0 True 3 2 Antoninek 10 +250000.0 True 2 4 Wilda 54 +269000.0 True 3 1 Wilda 68 +350000.0 True 4 4 Piątkowo 76 +360000.0 True 3 1 Grunwald 49 +260000.0 True 2 0 Rataje 46 +350000.0 True 2 4 Jeżyce 56 +263000.0 True 2 1 Rataje 44 +285000.0 True 2 2 Centrum 52 +285000.0 True 2 2 Łazarz 52 +429000.0 True 4 2 Grunwald 92 +211190.0 False 2 0 Podolany 78 +219000.0 True 2 3 Wilda 40 +820000.0 True 4 1 Grunwald 133 +299000.0 True 2 1 Centrum 11 +288000.0 True 2 4 Naramowice 44 +820000.0 True 4 1 Grunwald 133 +470000.0 True 4 2 Sołacz 87 +364000.0 True 3 4 Nowe 90 +706655.0 False 3 2 Nowe 45 +425000.0 True 3 1 Rataje 70 +248000.0 True 2 2 Winogrady 80 +260000.0 True 3 10 Śródka 48 +289000.0 True 2 0 Grunwald 80 +389000.0 True 3 4 Nowe 84 +253000.0 True 2 0 Łazarz 10 +449000.0 False 5 0 Szczepankowo 68 +225288.0 False 2 1 Rataje 91 +389528.0 False 2 2 Stare 87 +481903.0 False 3 2 Stare 53 +349000.0 False 4 0 Szczepankowo 29 +534523.0 False 3 2 Stare 62 +465538.0 False 3 1 Stare 78 +263000.0 True 2 0 Wilda 75 +370000.0 True 4 4 Piątkowo 76 +305000.0 True 3 3 Winogrady 60 +180000.0 True 3 2 Wilda 35 +189000.0 True 2 4 Wilda 35 +357692.0 False 3 2 Starołęka 31 +282994.0 False 2 0 Starołęka 59 +211190.0 False 2 0 Piątkowo 78 +349000.0 False 4 0 Szczepankowo 29 +277823.0 False 2 2 Podolany 70 +424377.0 False 4 2 Starołęka 14 +282944.0 False 2 0 Starołęka 59 +282944.0 False 2 0 Starołęka 59 +245000.0 True 2 7 Rataje 44 +570000.0 True 4 0 Jeżyce 90 +720000.0 True 4 7 Jeżyce 90 +237000.0 True 2 2 Dębiec 44 +329000.0 True 3 3 Piątkowo 60 +270000.0 True 3 3 Stare 47 +487000.0 True 3 0 Naramowice 83 +271000.0 True 2 3 Stare 37 +372000.0 False 4 1 Grunwald 87 +487000.0 True 3 0 Stare 11 +326000.0 True 2 1 Sołacz 39 +270000.0 True 2 10 Śródka 48 +349000.0 True 3 3 Rataje 63 +285000.0 True 2 2 Grunwald 52 +262500.0 True 4 0 Wilda 75 +350000.0 True 2 1 Rataje 80 +199000.0 True 2 3 Grunwald 35 +349000.0 False 4 0 Szczepankowo 29 +250000.0 True 2 3 Wilda 10 +234000.0 True 2 7 Wilda 46 +210000.0 True 2 1 Wilda 65 +249000.0 True 2 10 Grunwald 43 +469000.0 True 2 1 Winogrady 30 +235000.0 True 2 0 Nowe 10 +265000.0 True 2 0 Centrum 40 +329000.0 True 3 13 Rataje 65 +265000.0 True 2 2 Piątkowo 70 +350000.0 True 3 0 Stare 10 +307000.0 True 2 4 Stare 49 +315000.0 True 3 0 Stare 63 +350000.0 True 3 0 Rataje 63 +690000.0 True 2 1 Stare 20 +423000.0 True 2 2 Wilda 49 +250000.0 True 2 6 Grunwald 31 +292000.0 True 3 2 Winogrady 47 +249000.0 True 2 10 Grunwald 42 +350000.0 True 2 3 Rataje 52 +780000.0 True 3 0 Grunwald 87 +1000000.0 True 15 5 Wilda 50 +535000.0 True 2 2 Centrum 55 +285200.0 True 2 0 Stare 46 +434201.0 True 4 1 Nowe 54 +344152.0 True 3 0 Nowe 80 +396000.0 True 3 1 Wilda 50 +240000.0 True 2 16 Rataje 36 +390000.0 True 3 4 Piątkowo 74 +288000.0 True 2 4 Naramowice 22 +518000.0 True 4 0 Wilda 41 +320000.0 True 4 3 Stare 40 +449000.0 True 5 3 Wilda 97 +249000.0 True 2 10 Grunwald 42 +289000.0 True 3 4 Winogrady 48 +289000.0 True 2 7 Jeżyce 80 +330715.0 True 2 2 Wilda 13 +97000.0 True 2 4 Wilda 80 +285000.0 True 2 2 Łazarz 20 +389000.0 True 3 4 Piątkowo 69 +249000.0 True 2 4 Rataje 44 +409000.0 True 3 1 Rataje 62 +240000.0 True 2 2 Dębiec 48 +289000.0 True 3 4 Stare 47 +270000.0 True 3 10 Grunwald 52 +389000.0 True 3 4 Piątkowo 69 +179000.0 True 2 0 Grunwald 34 +364000.0 False 3 6 Grunwald 64 +410000.0 True 2 4 Jeżyce 43 +590000.0 True 3 3 Jeżyce 30 +325000.0 True 3 2 Jeżyce 64 +398000.0 True 3 3 Łazarz 96 +255000.0 True 2 2 Wilda 72 +329000.0 True 2 1 Naramowice 40 +290000.0 True 2 6 Winiary 49 +319875.0 False 2 8 Grunwald 18 +356251.9 False 3 13 Grunwald 20 +319875.0 False 2 7 Grunwald 18 +350557.33 False 2 13 Grunwald 58 +338325.0 False 2 13 Grunwald 5 +329763.26 False 2 9 Grunwald 94 +324400.97 False 2 7 Grunwald 94 +388352.0 False 3 7 Grunwald 60 +347633.0 False 3 10 Grunwald 20 +409713.0 False 3 11 Grunwald 62 +330368.0 False 2 12 Grunwald 62 +347839.75 False 2 12 Grunwald 58 +347193.22 False 3 11 Grunwald 7 +350506.16 False 3 11 Grunwald 20 +342405.13 False 2 11 Grunwald 58 +319875.0 False 2 9 Grunwald 18 +341703.96 False 3 8 Grunwald 21 +336969.98 False 2 10 Grunwald 58 +413044.0 False 3 12 Grunwald 62 +341703.96 False 3 9 Grunwald 21 +325206.0 False 2 10 Grunwald 62 +338111.0 False 2 15 Grunwald 62 +424977.14 False 4 5 Grunwald 20 +327787.0 False 2 11 Grunwald 62 +353378.74 False 3 12 Grunwald 20 +332949.0 False 2 13 Grunwald 62 +383760.0 False 3 6 Grunwald 60 +335530.0 False 2 14 Grunwald 62 +387040.0 False 3 5 Grunwald 60 +302985.6 False 2 4 Grunwald 18 +421375.5 False 4 4 Grunwald 20 +410780.0 False 3 3 Grunwald 44 +417773.83 False 4 3 Grunwald 20 +303286.5 False 2 3 Grunwald 13 +302038.4 False 2 3 Grunwald 2 +319055.27 False 3 3 Grunwald 21 +414352.0 False 3 4 Grunwald 44 +417807.03 False 4 4 Grunwald 7 +414172.54 False 4 2 Grunwald 20 +352390.0 False 2 12 Grunwald 80 +377200.0 False 3 3 Grunwald 60 +314089.0 False 2 5 Grunwald 49 +339072.0 False 2 9 Grunwald 98 +321812.5 False 2 8 Grunwald 49 +500203.02 False 4 10 Grunwald 73 +355080.0 False 2 13 Grunwald 80 +325184.0 False 2 11 Grunwald 81 +297420.8 False 2 3 Grunwald 24 +506566.5 False 4 11 Grunwald 73 +335722.5 False 2 12 Grunwald 5 +349700.0 False 2 11 Grunwald 80 +330517.5 False 2 10 Grunwald 5 +495722.51 False 4 9 Grunwald 99 +426416.8 False 4 6 Grunwald 20 +327081.85 False 2 8 Grunwald 94 +307080.0 False 2 5 Grunwald 18 +305793.0 False 2 4 Grunwald 13 +380480.0 False 3 4 Grunwald 60 +312198.0 False 2 6 Grunwald 18 +410665.2 False 4 2 Grunwald 7 +333231.99 False 3 7 Grunwald 21 +514939.5 False 4 13 Grunwald 73 +317880.0 False 2 2 Grunwald 98 +510753.0 False 4 12 Grunwald 73 +333120.0 False 2 11 Grunwald 5 +324387.0 False 2 9 Grunwald 49 +311514.5 False 2 4 Grunwald 49 +495722.51 False 4 8 Grunwald 99 +331125.0 False 2 5 Grunwald 98 +495782.26 False 4 7 Grunwald 99 +328476.0 False 2 4 Grunwald 98 +316848.0 False 2 6 Grunwald 52 +442803.77 False 4 5 Grunwald 7 +315819.0 False 2 5 Grunwald 13 +293436.18 False 2 1 Grunwald 15 +435784.0 False 3 5 Grunwald 44 +414235.76 False 4 3 Grunwald 7 +407208.0 False 3 2 Grunwald 44 +579000.0 True 4 3 Naramowice 97 +410000.0 True 2 5 Rataje 53 +199000.0 True 2 4 Grunwald 20 +375000.0 True 2 3 Grunwald 51 +350000.0 True 3 0 Naramowice 59 +289000.0 True 3 4 Winogrady 47 +240000.0 True 2 16 Rataje 36 +350000.0 True 3 1 Naramowice 51 +238000.0 True 3 2 Warszawskie 48 +277823.0 False 2 2 Podolany 70 +372000.0 True 4 1 Nadolnik 125 +410000.0 True 2 5 Rataje 53 +249000.0 True 2 4 Rataje 44 +420000.0 True 2 1 Naramowice 50 +420000.0 True 2 3 Naramowice 50 +339000.0 True 2 2 Stare 53 +298000.0 True 3 1 Nowe 30 +250000.0 True 3 0 Stare 45 +475000.0 True 4 4 Naramowice 50 +329000.0 True 3 1 Jeżyce 112 +439000.0 True 3 3 Grunwald 10 +250000.0 True 2 6 Winogrady 42 +259000.0 True 3 1 Grunwald 48 +375000.0 True 2 7 Piątkowo 90 +295000.0 True 2 7 Stare 10 +370000.0 True 4 4 Piątkowo 60 +325000.0 True 3 3 Łazarz 62 +375000.0 True 3 1 Nowe 63 +390000.0 True 4 4 Piątkowo 74 +288000.0 True 3 4 Stare 30 +468000.0 True 2 3 Grunwald 60 +250000.0 True 2 6 Winogrady 42 +350000.0 True 2 2 Jeżyce 46 +292000.0 True 3 2 Winogrady 30 +310000.0 True 2 1 Nowe 40 +289000.0 True 3 4 Winogrady 47 +405900.0 True 3 2 Stare 82 +149000.0 True 3 5 Nowe 56 +326000.0 True 2 1 Sołacz 39 +350000.0 True 2 2 Jeżyce 47 +224343.0 False 2 4 Starołęka 35 +362220.0 False 3 3 Starołęka 60 +287394.0 False 2 2 Starołęka 50 +320739.0 False 3 1 Starołęka 56 +177000.0 True 2 2 Dębiec 25 +313000.0 True 2 1 Górczyn 48 +313000.0 True 2 1 Dębiec 48 +429000.0 True 3 4 Rataje 79 +643720.0 True 4 0 Stare 60 +325000.0 True 2 3 Stare 60 +319000.0 True 2 0 Grunwald 20 +364000.0 True 3 1 Nowe 67 +285000.0 True 2 2 Łazarz 52 +339000.0 True 2 2 Centrum 53 +279000.0 True 2 0 Naramowice 43 +350000.0 True 2 4 Jeżyce 53 +419000.0 True 3 1 Piątkowo 74 +195000.0 True 2 3 Zawady 35 +390000.0 True 2 0 Centrum 60 +177000.0 True 2 2 Dębiec 70 +279000.0 True 2 1 Stare 60 +489000.0 True 4 2 Wilda 120 +299000.0 True 2 1 Jeżyce 32 +205000.0 True 2 4 Wilda 27 +362000.0 True 2 1 Centrum 50 +285000.0 True 2 2 Łazarz 52 +998000.0 True 6 2 Stare 161 +259000.0 True 3 2 Grunwald 45 +439000.0 True 2 3 Rataje 53 +550000.0 True 4 1 Górczyn 90 +310000.0 True 3 10 Nowe 40 +355000.0 True 3 2 Stare 64 +252000.0 True 2 9 Grunwald 50 +659000.0 True 3 2 Nowe 60 +307000.0 True 2 4 Piątkowo 49 +347900.0 True 3 3 Nowe 10 +229000.0 True 2 3 Stare 56 +569000.0 True 4 0 Wilda 50 +136000.0 True 2 1 Nowe 43 +102500.0 True 2 3 Nowe 80 +485000.0 True 4 2 Grunwald 89 +360000.0 True 3 3 Nowe 63 +339000.0 True 3 3 Stare 90 +285000.0 True 2 0 Łazarz 49 +299000.0 True 2 1 Centrum 52 +429999.0 True 3 3 Centrum 20 +429999.0 True 3 3 Centrum 20 +395000.0 True 3 3 Wilda 75 +307000.0 True 2 4 Piątkowo 49 +326000.0 True 2 4 Łazarz 80 +382280.0 True 3 3 Centrum 50 +233239.0 False 2 2 Podolany 87 +400608.0 False 3 2 Podolany 48 +422604.0 False 4 2 Podolany 24 +350064.0 False 3 2 Podolany 84 +349420.0 False 3 2 Podolany 73 +275008.0 False 2 2 Podolany 1 +255762.0 False 2 2 Podolany 72 +257400.0 False 2 2 Podolany 44 +307710.0 False 2 2 Podolany 60 +338188.0 False 3 2 Podolany 81 +258336.0 False 2 2 Podolany 16 +370948.0 False 4 2 Podolany 41 +358605.0 False 3 2 Podolany 30 +245934.0 False 2 2 Podolany 4 +233941.0 False 2 1 Podolany 99 +401544.0 False 3 1 Podolany 64 +424008.0 False 4 1 Podolany 48 +350181.0 False 3 1 Podolany 86 +349537.0 False 3 1 Podolany 75 +275710.0 False 2 1 Podolany 13 +256756.0 False 2 1 Podolany 89 +258102.0 False 2 1 Podolany 12 +255000.0 True 2 3 Jeżyce 38 +300222.0 False 2 1 Podolany 22 +308412.0 False 2 1 Podolany 72 +338305.0 False 3 1 Podolany 83 +259038.0 False 2 1 Podolany 28 +371884.0 False 4 1 Podolany 57 +359541.0 False 3 1 Podolany 46 +234636.0 False 2 1 Podolany 16 +234234.0 False 2 0 Podolany 4 +401719.0 False 3 0 Podolany 67 +423715.0 False 4 0 Podolany 43 +350181.0 False 3 0 Podolany 86 +249537.0 False 3 0 Podolany 75 +276061.0 False 2 0 Podolany 19 +257341.0 False 2 0 Podolany 99 +258453.0 False 2 0 Podolany 18 +220837.0 False 2 0 Podolany 75 +419000.0 True 2 7 Grunwald 20 +419000.0 True 3 4 Wilda 60 +379000.0 True 2 3 Winogrady 48 +315000.0 True 3 0 Piątkowo 60 +339000.0 True 3 1 Rataje 67 +270000.0 True 2 4 Grunwald 38 +268000.0 True 2 5 Rataje 42 +1500000.0 True 3 5 Centrum 68 +264000.0 True 3 4 Nowe 53 +432000.0 True 4 1 Grunwald 72 +449900.0 True 3 2 Stare 81 +295000.0 True 2 1 Nowe 39 +290000.0 True 2 6 Sołacz 49 +307000.0 True 2 4 Piątkowo 49 +285000.0 True 2 3 Piątkowo 49 +285000.0 True 2 3 Wilda 60 +519000.0 True 3 1 Rataje 50 +264000.0 True 3 4 Rataje 53 +318000.0 True 2 4 Piątkowo 49 +325000.0 True 3 3 Sołacz 40 +377685.0 False 2 4 Podolany 4 +377685.0 False 3 4 Podolany 67 +423715.0 False 4 0 Podolany 43 +350181.0 False 3 0 Podolany 86 +349537.0 False 3 0 Podolany 75 +276061.0 False 2 0 Podolany 19 +242990.0 False 2 0 Podolany 18 +283645.0 False 2 0 Podolany 39 +308763.0 False 2 0 Podolany 78 +338305.0 False 3 0 Podolany 83 +480000.0 True 2 2 Centrum 56 +499000.0 True 2 2 Nowe 36 +299000.0 True 2 16 Rataje 49 +355000.0 True 3 2 Stare 64 +210000.0 True 2 0 Grunwald 52 +277098.0 True 2 0 Nowe 59 +410000.0 True 3 1 Górczyn 82 +399000.0 True 3 2 Górczyn 91 +390000.0 True 3 1 Łazarz 75 +370000.0 True 2 0 Górczyn 65 +239000.0 True 2 3 Piątkowo 59 +185000.0 True 2 8 Wilda 38 +432000.0 True 3 0 Wilda 72 +360000.0 True 3 4 Rataje 69 +259330.0 False 2 0 Podolany 33 +372996.0 False 4 0 Podolany 76 +360000.0 True 3 2 Rataje 69 +370000.0 True 4 4 Piątkowo 76 +338579.0 False 3 0 Podolany 56 +231550.0 False 2 0 Podolany 10 +325000.0 True 2 1 Jeżyce 56 +355000.0 True 2 4 Jeżyce 56 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J.item()\n", + "\n", + "# Wersja macierzowa gradientu funkcji kosztu\n", + "def dJMx(theta,X,y):\n", + " return 1.0 / len(y) * (X.T * (X * theta - y)) \n", + "\n", + "# Implementacja algorytmu gradientu prostego za pomocą numpy i macierzy\n", + "def GDMx(fJ, fdJ, theta, X, y, alpha=0.1, eps=10**-3):\n", + " current_cost = fJ(theta, X, y)\n", + " logs = [[current_cost, theta]]\n", + " while True:\n", + " theta = theta - alpha * fdJ(theta, X, y) # implementacja wzoru\n", + " current_cost, prev_cost = fJ(theta, X, y), current_cost\n", + " if current_cost > 10000:\n", + " break\n", + " if abs(prev_cost - current_cost) <= eps:\n", + " break\n", + " logs.append([current_cost, theta]) \n", + " return theta, logs\n", + "\n", + "thetaStartMx = np.matrix([0, 0]).reshape(2, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + " \n", 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\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = regdotsMx(XMx, yMx)\n", + "theta_e1, logs1 = GDMx(JMx, dJMx, thetaStartMx, XMx, yMx, alpha=0.01, eps=0.01)\n", + "reglineMx(fig, hMx, theta_e1, XMx)\n", + "theta_e2, logs2 = GDMx(JMx, dJMx, thetaStartMx, XMx, yMx, alpha=0.01, eps=0.000001)\n", + "reglineMx(fig, hMx, theta_e2, XMx)\n", + "legend(fig)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$$\\theta_{10^{-2}} = \\left[\\begin{array}{r}0.0511 \\\\ 0.7957 \\\\ \\end{array}\\right]\\quad\\theta_{10^{-6}} = \\left[\\begin{array}{r}-3.8407 \\\\ 1.1875 \\\\ \\end{array}\\right]$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "display(Math(r'\\theta_{10^{-2}} = ' + LatexMatrix(theta_e1) +\n", + " r'\\quad\\theta_{10^{-6}} = ' + LatexMatrix(theta_e2)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Długość kroku ($\\alpha$)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Jak zmienia się koszt w kolejnych krokach w zależności od alfa\n", + "\n", + "def costchangeplot(logs):\n", + " fig = pl.figure(figsize=(16*.6, 9*.6))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + " ax.set_xlabel('krok')\n", + " ax.set_ylabel(r'$J(\\theta)$')\n", + "\n", + " X = np.arange(0, 100, 1)\n", + " Y = [logs[step][0] if step < len(logs) else None for step in X]\n", + " ax.plot(X, Y, linewidth='2', label=(r'$J(\\theta)$'))\n", + " return fig\n", + "\n", + "def slide1(alpha):\n", + " best_theta, logs = GDMx(JMx, dJMx, thetaStartMx, XMx, yMx, alpha=alpha, eps=0.0001)\n", + " fig = costchangeplot(logs)\n", + " legend(fig)\n", + "\n", + "sliderAlpha1 = widgets.FloatSlider(min=0.01, max=0.03, step=0.001, value=0.02, description=r'$\\alpha$', width=300)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "98679fb9d83947408fe409f5eaeec810", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

Failed to display Jupyter Widget of type interactive.

\n", + "

\n", + " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", + " that the widgets JavaScript is still loading. If this message persists, it\n", + " likely means that the widgets JavaScript library is either not installed or\n", + " not enabled. See the Jupyter\n", + " Widgets Documentation for setup instructions.\n", + "

\n", + "

\n", + " If you're reading this message in another notebook frontend (for example, a static\n", + " rendering on GitHub or NBViewer),\n", + " it may mean that your frontend doesn't currently support widgets.\n", + "

\n" + ], + "text/plain": [ + "interactive(children=(FloatSlider(value=0.02, description=u'$\\\\alpha$', max=0.03, min=0.01, step=0.001), Button(description=u'Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "widgets.interact_manual(slide1, alpha=sliderAlpha1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 2.2. Normalizacja danych" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Użyjemy danych z „Gratka flats challenge 2017”.\n", + "\n", + "Rozważmy model $h(x) = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2$, w którym cena mieszkania prognozowana jest na podstawie liczby pokoi $x_1$ i metrażu $x_2$:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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priceroomssqrMetres
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\n", + "
" + ], + "text/plain": [ + " price rooms sqrMetres\n", + "0 476118.00 3 78\n", + "1 459531.00 3 62\n", + "2 411557.00 3 15\n", + "3 496416.00 4 14\n", + "4 406032.00 3 15\n", + "5 450026.00 3 80\n", + "6 571229.15 2 39\n", + "7 325000.00 3 54\n", + "8 268229.00 2 90\n", + "9 604836.00 4 40" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Wczytanie danych przy pomocy biblioteki pandas\n", + "import pandas\n", + "alldata = pandas.read_csv('data_flats.tsv', header=0, sep='\\t',\n", + " usecols=['price', 'rooms', 'sqrMetres'])\n", + "alldata[:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def show_mins_and_maxs(XMx):\n", + " mins = np.amin(XMx, axis=0).tolist()[0] # wartości minimalne\n", + " maxs = np.amax(XMx, axis=0).tolist()[0] # wartości maksymalne\n", + " for i, (xmin, xmax) in enumerate(zip(mins, maxs)):\n", + " display(Math(\n", + " r'${:.2F} \\leq x_{} \\leq {:.2F}$'.format(xmin, i, xmax)))" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przygotowanie danych\n", + "\n", + "import numpy as np\n", + "\n", + "%matplotlib inline\n", + "\n", + "data2 = np.matrix(alldata[['rooms', 'sqrMetres', 'price']])\n", + "\n", + "m, n_plus_1 = data2.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data2[:, 0:n]\n", + "\n", + "XMx2 = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n", + "yMx2 = np.matrix(data2[:, -1]).reshape(m, 1) / 1000.0" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Cechy w danych treningowych przyjmują wartości z zakresu:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$$1.00 \\leq x_0 \\leq 1.00$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$$2.00 \\leq x_1 \\leq 7.00$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$$12.00 \\leq x_2 \\leq 196.00$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "show_mins_and_maxs(XMx2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Jak widzimy, $x_2$ przyjmuje wartości dużo większe niż $x_1$.\n", + "Powoduje to, że wykres funkcji kosztu jest bardzo „spłaszczony” wzdłuż jednej z osi:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def contour_plot(X, y, rescale=10**8):\n", + " theta0_vals = np.linspace(-100000, 100000, 100)\n", + " theta1_vals = np.linspace(-100000, 100000, 100)\n", + "\n", + " J_vals = np.zeros(shape=(theta0_vals.size, theta1_vals.size))\n", + " for t1, element in enumerate(theta0_vals):\n", + " for t2, element2 in enumerate(theta1_vals):\n", + " thetaT = np.matrix([1.0, element, element2]).reshape(3,1)\n", + " J_vals[t1, t2] = JMx(thetaT, X, y) / rescale\n", + " \n", + " pl.figure()\n", + " pl.contour(theta0_vals, theta1_vals, J_vals.T, np.logspace(-2, 3, 20))\n", + " pl.xlabel(r'$\\theta_1$')\n", + " pl.ylabel(r'$\\theta_2$')" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", 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"contour_plot(XMx2, yMx2, rescale=10**10)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Skalowanie" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Będziemy dążyć do tego, żeby każda z cech przyjmowała wartości w podobnym zakresie.\n", + "\n", + "W tym celu przeskalujemy wartości każdej z cech, dzieląc je przez wartość maksymalną:\n", + "\n", + "$$ \\hat{x_i}^{(j)} := \\frac{x_i^{(j)}}{\\max_j x_i^{(j)}} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$$1.00 \\leq x_0 \\leq 1.00$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$$0.29 \\leq x_1 \\leq 1.00$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$$0.06 \\leq x_2 \\leq 1.00$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "XMx2_scaled = XMx2 / np.amax(XMx2, axis=0)\n", + "\n", + "show_mins_and_maxs(XMx2_scaled)" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", 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" \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " 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\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "contour_plot(XMx2_scaled, yMx2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Normalizacja średniej" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Będziemy dążyć do tego, żeby dodatkowo średnia wartość każdej z cech była w okolicach $0$.\n", + "\n", + "W tym celu oprócz przeskalowania odejmiemy wartość średniej od wartości każdej z cech:\n", + "\n", + "$$ \\hat{x_i}^{(j)} := \\frac{x_i^{(j)} - \\mu_i}{\\max_j x_i^{(j)}} $$" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$$0.00 \\leq x_0 \\leq 0.00$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$$-0.10 \\leq x_1 \\leq 0.62$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$$-0.23 \\leq x_2 \\leq 0.70$$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "XMx2_norm = (XMx2 - np.mean(XMx2, axis=0)) / np.amax(XMx2, axis=0)\n", + "\n", + "show_mins_and_maxs(XMx2_norm)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", 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\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "contour_plot(XMx2_norm, yMx2)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 2.3. Regresja logistyczna" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + " * Uwaga: _regresja_ logistyczna jest algorytmem dla problemów _klasyfikacji_ (nie _regresji_, wbrew nazwie)!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Klasyfikacja dwuklasowa" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\n", + "\n", + "### Przykład: kosaciec szczecinkowy (_Iris setosa_)\n", + "\n", + "Mamy dane dotyczące długości płatków i chcielibyśmy na tej podstawie określić, czy jest to roślina z gatunku _Iris setosa_" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " dł. płatka Iris setosa?\n", + "0 1.4 1.0\n", + "1 1.5 1.0\n", + "2 5.6 0.0\n", + "3 5.1 0.0\n", + "4 4.5 0.0\n", + "5 5.1 0.0" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas\n", + "data_iris_setosa = (\n", + " pandas.read_csv('iris.csv', usecols=['pł.dł.', 'Gatunek'])\n", + " .apply(lambda x: [x[0], 1 if x[1] == 'Iris-setosa' else 0], axis=1))\n", + "data_iris_setosa.columns = ['dł. płatka', 'Iris setosa?']\n", + "data_iris_setosa[:6]" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Rysowanie progu\n", + "def threshold(fig, theta):\n", + " x_thr = (0.5 - theta.item(0)) / theta.item(1)\n", + " ax = fig.axes[0]\n", + " ax.plot([x_thr, x_thr], [-1, 2],\n", + " color='orange', linestyle='dashed',\n", + " label=u'próg: $x={:.2F}$'.format(x_thr))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Spróbujmy zastosować regresję liniową:" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "m, n_plus_1 = data_iris_setosa.values.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data_iris_setosa.values[:, 0:n].reshape(m, n)\n", + "\n", + "XMx3 = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n", + "yMx3 = np.matrix(data_iris_setosa.values[:, 1]).reshape(m, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " 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setosa?')\n", + "theta_e3, logs3 = GDMx(JMx, dJMx, thetaStartMx, XMx3, yMx3, alpha=0.03, eps=0.000001)\n", + "reglineMx(fig, hMx, theta_e3, XMx3)\n", + "threshold(fig, theta_e3)\n", + "legend(fig)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + " * Krzywa regresji liniowej jest niezbyt dopasowana do danych klasyfikacyjnych.\n", + " * Zastosowanie progu $y = 0.5$ nie zawsze pomaga uzyskać sensowny rezultat.\n", + " * $h(x)$ może przyjmować wartości mniejsze od $0$ i większe od $1$ – jak interpretować takie wyniki?\n", + "\n", + "Wniosek: w przypadku problemów klasyfikacyjnych regresja liniowa nie wydaje się najlepszym rozwiązaniem." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "Funkcja logistyczna (sigmoidalna):\n", + "\n", + "$$g(x) = \\dfrac{1}{1+e^{-x}}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [], + "source": [ + "def logistic(x):\n", + " return 1.0 / (1.0 + np.exp(-x))" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "def plot_logistic():\n", + " x = np.linspace(-5,5,200)\n", + " y = logistic(x)\n", + "\n", + " fig = plt.figure(figsize=(7,5))\n", + " ax = fig.add_subplot(111)\n", + " plt.ylim(-.1,1.1)\n", + " ax.plot(x, y, linewidth='2')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Wykres funkcji logistycznej $g(x) = \\dfrac{1}{1+e^{-x}}$:" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " 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"" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_logistic()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Funkcja regresji logistycznej:\n", + "\n", + "$$h_\\theta(x) = g(\\theta^T \\, x) = \\dfrac{1}{1 + e^{-\\theta^T x}}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Wersja macierzowa:\n", + "\n", + "$$h_\\theta(X) = g(X \\, \\theta) = \\dfrac{1}{1 + e^{-X \\theta}}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "# Funkcja regresji logistcznej\n", + "def h(theta, X):\n", + " return 1.0/(1.0 + np.exp(-X * theta))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Funkcja kosztu dla regresji logistycznej:\n", + "\n", + "$$J(\\theta) = -\\dfrac{1}{m} \\left( \\sum_{i=1}^{m} y^{(i)} \\log h_\\theta( x^{(i)} ) + \\left( 1 - y^{(i)} \\right) \\log \\left( 1 - h_\\theta (x^{(i)}) \\right) \\right)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Gradient dla regresji logistycznej (wersja macierzowa):\n", + "\n", + "$$\\nabla J(\\theta) = \\frac{1}{|\\vec y|} X^T \\left( h_\\theta(X) - \\vec y \\right)$$\n", + "\n", + "(Jedyna różnica między gradientem dla regresji logistycznej a gradientem dla regresji liniowej to postać $h_\\theta$)." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Funkcja kosztu dla regresji logistycznej\n", + "def J(h, theta, X, y):\n", + " m = len(y)\n", + " h_val = h(theta, X)\n", + " s1 = np.multiply(y, np.log(h_val))\n", + " s2 = np.multiply((1 - y), np.log(1 - h_val))\n", + " return -np.sum(s1 + s2, axis=0) / m" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [], + "source": [ + "# Gradient dla regresji logistycznej\n", + "def dJ(h, theta, X, y):\n", + " return 1.0 / len(y) * (X.T * (h(theta, X) - y))" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Metoda gradientu prostego dla regresji logistycznej\n", + "def GD(h, fJ, fdJ, theta, X, y, alpha=0.01, eps=10**-3, maxSteps=10000):\n", + " errorCurr = fJ(h, theta, X, y)\n", + " errors = [[errorCurr, theta]]\n", + " while True:\n", + " # oblicz nowe theta\n", + " theta = theta - alpha * fdJ(h, theta, X, y)\n", + " # raportuj poziom błędu\n", + " errorCurr, errorPrev = fJ(h, theta, X, y), errorCurr\n", + " # kryteria stopu\n", + " if abs(errorPrev - errorCurr) <= eps:\n", + " break\n", + " if len(errors) > maxSteps:\n", + " break\n", + " errors.append([errorCurr, theta]) \n", + " return theta, errors" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('error =', matrix([[ 0.05755617]]))\n", + "('theta =', matrix([[ 5.02530461],\n", + " [-1.99174803]]))\n" + ] + } + ], + "source": [ + "# Uruchomienie metody gradientu prostego dla regresji logistycznej\n", + "thetaBest, errors = GD(h, J, dJ, thetaStartMx, XMx3, yMx3, \n", + " alpha=0.1, eps=10**-7, maxSteps=1000)\n", + "print(\"error =\", errors[-1][0])\n", + "print(\"theta =\", thetaBest)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Funkcja regresji logistycznej (wersja skalarna)\n", + "def scalar_logistic_regression_function(theta, x):\n", + " return 1.0/(1.0 + np.exp(-(theta.item(0) + theta.item(1) * x)))\n", + "\n", + "# Rysowanie progu\n", + "def threshold_val(fig, x_thr):\n", + " ax = fig.axes[0]\n", + " ax.plot([x_thr, x_thr], [-1, 2],\n", + " color='orange', linestyle='dashed',\n", + " label=u'próg: $x={:.2F}$'.format(x_thr))\n", + "\n", + "# Wykres krzywej regresji logistycznej\n", + "def logistic_regline(fig, theta, X):\n", + " ax = fig.axes[0]\n", + " x0 = np.min(X[:, 1]) - 1.0\n", + " x1 = np.max(X[:, 1]) + 1.0\n", + " Arg = np.arange(x0, x1, 0.1)\n", + " Val = scalar_logistic_regression_function(theta, Arg)\n", + " ax.plot(Arg, Val, linewidth='2')" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "scrolled": true, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " 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\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = regdotsMx(XMx3, yMx3, xlabel='x', ylabel='Iris setosa?')\n", + "logistic_regline(fig, thetaBest, XMx3)\n", + "threshold_val(fig, 2.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Traktujemy wartość $h_\\theta(x)$ jako prawdopodobieństwo, że cecha przyjmie wartość pozytywną:\n", + "\n", + "$$ h_\\theta(x) = P(y = 1 \\, | \\, x; \\theta) $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Dwuklasowa regresja logistyczna: więcej cech" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Weźmy pod uwagę następujące cechy:\n", + " * długość dziełek kielicha\n", + " * szerokość działek kielicha\n", + " * długość płatka\n", + " * szerokość płatka" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
slswplpwIris setosa?
05.23.41.40.21.0
15.13.71.50.41.0
26.73.15.62.40.0
36.53.25.12.00.0
44.92.54.51.70.0
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\n", + "
" + ], + "text/plain": [ + " sl sw pl pw Iris setosa?\n", + "0 5.2 3.4 1.4 0.2 1.0\n", + "1 5.1 3.7 1.5 0.4 1.0\n", + "2 6.7 3.1 5.6 2.4 0.0\n", + "3 6.5 3.2 5.1 2.0 0.0\n", + "4 4.9 2.5 4.5 1.7 0.0\n", + "5 6.0 2.7 5.1 1.6 0.0" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas\n", + "src_cols = ['sl', 'sw', 'pl', 'pw', 'Gatunek']\n", + "trg_cols = ['sl', 'sw', 'pl', 'pw', 'Iris setosa?']\n", + "data_iris_setosa_multi = (\n", + " pandas.read_csv('iris.csv', usecols=src_cols)\n", + " .apply(lambda x: [x[0], x[1], x[2], x[3], 1 if x[4] == 'Iris-setosa' else 0], axis=1))\n", + "data_iris_setosa_multi.columns = trg_cols\n", + "data_iris_setosa_multi[:6]" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import seaborn" + ] + }, + { + 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data_iris_setosa_multi.columns if c != 'Iris setosa?'], \n", + " hue='Iris setosa?', size=1.5, aspect=1.75)" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1. 5.2 3.4 1.4 0.2]\n", + " [ 1. 5.1 3.7 1.5 0.4]\n", + " [ 1. 6.7 3.1 5.6 2.4]\n", + " [ 1. 6.5 3.2 5.1 2. ]\n", + " [ 1. 4.9 2.5 4.5 1.7]\n", + " [ 1. 6. 2.7 5.1 1.6]]\n", + "[[ 1.]\n", + " [ 1.]\n", + " [ 0.]\n", + " [ 0.]\n", + " [ 0.]\n", + " [ 0.]]\n" + ] + } + ], + "source": [ + "# Przygotowanie danych\n", + "m, n_plus_1 = data_iris_setosa_multi.values.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data_iris_setosa_multi.values[:, 0:n].reshape(m, n)\n", + "\n", + "XMx4 = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n", + "yMx4 = np.matrix(data_iris_setosa_multi.values[:, n]).reshape(m, 1)\n", + "\n", + "print(XMx4[:6])\n", + "print(yMx4[:6])" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Podział danych na zbiór trenujący i testowy\n", + "XTrain, XTest = XMx4[:100], XMx4[100:]\n", + "yTrain, yTest = yMx4[:100], yMx4[100:]\n", + "\n", + "# Macierz parametrów początkowych\n", + "thetaTemp = np.ones(5).reshape(5,1)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('error =', matrix([[ 0.006797]]))\n", + "('theta =', matrix([[ 1.11414027],\n", + " [ 0.14887292],\n", + " [ 2.13284493],\n", + " [-2.89324615],\n", + " [-0.66543637]]))\n" + ] + } + ], + "source": [ + "thetaBest, errors = GD(h, J, dJ, thetaTemp, XTrain, yTrain, \n", + " alpha=0.1, eps=10**-7, maxSteps=1000)\n", + "print(\"error =\", errors[-1][0])\n", + "print(\"theta =\", thetaBest)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Funkcja decyzyjna regresji logistycznej\n", + "\n", + "$$ c = \\left\\{ \n", + "\\begin{array}{ll}\n", + "1, & \\mbox{gdy } P(y=1 \\, | \\, x; \\theta) > 0.5 \\\\\n", + "0 & \\mbox{w przeciwnym przypadku}\n", + "\\end{array}\\right.\n", + "$$\n", + "\n", + "$$ P(y=1 \\,| \\, x; \\theta) = h_\\theta(x) $$" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('theta =', matrix([[ 1.11414027],\n", + " [ 0.14887292],\n", + " [ 2.13284493],\n", + " [-2.89324615],\n", + " [-0.66543637]]))\n", + "('x0 =', matrix([[ 1. , 7.3, 2.9, 6.3, 1.8]]))\n", + "('h(x0) =', 1.606143695982493e-05)\n", + "('c(x0) =', (0, 1.606143695982493e-05), '\\n')\n" + ] + } + ], + "source": [ + "def classifyBi(theta, X):\n", + " prob = h(theta, X).item()\n", + " return (1, prob) if prob > 0.5 else (0, prob)\n", + "\n", + "print(\"theta =\", thetaBest)\n", + "print(\"x0 =\", XTest[0])\n", + "print(\"h(x0) =\", h(thetaBest, XTest[0]).item())\n", + "print(\"c(x0) =\", classifyBi(thetaBest, XTest[0]), \"\\n\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Skuteczność" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(0, '<=>', 0, '-- prob:', 0.0)\n", + "(1, '<=>', 1, '-- prob:', 0.9816)\n", + "(0, '<=>', 0, '-- prob:', 0.0001)\n", + "(0, '<=>', 0, '-- prob:', 0.0005)\n", + "(0, '<=>', 0, '-- prob:', 0.0001)\n", + "(1, '<=>', 1, '-- prob:', 0.9936)\n", + "(0, '<=>', 0, '-- prob:', 0.0059)\n", + "(0, '<=>', 0, '-- prob:', 0.0992)\n", + "(0, '<=>', 0, '-- prob:', 0.0001)\n", + "(0, '<=>', 0, '-- prob:', 0.0001)\n", + "('\\nAccuracy:', 1.0)\n" + ] + } + ], + "source": [ + "acc = 0.0\n", + "for i, rest in enumerate(yTest):\n", + " cls, prob = classifyBi(thetaBest, XTest[i])\n", + " if i < 10:\n", + " print(int(yTest[i].item()), \"<=>\", cls, \"-- prob:\", round(prob, 4))\n", + " acc += cls == yTest[i].item()\n", + "\n", + "print(\"\\nAccuracy:\", acc / len(XTest))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 2.4. Wieloklasowa regresja logistyczna" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Przykład: gatunki irysów (kosaćców)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\n", + "\n", + "Kosaciec szczecinkowy (_Iris setosa_)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\n", + "\n", + "Kosaciec amerykański (_Iris virginica_)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\n", + "\n", + "Kosaciec różnobarwny (_Iris versicolor_)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Cechy:\n", + " * długość działek kielicha\n", + " * szerokość działek kielicha\n", + " * długość płatka\n", + " * szerokość płatka" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Wczytanie danych" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
slswplpwGatunek
05.23.41.40.2Iris-setosa
15.13.71.50.4Iris-setosa
26.73.15.62.4Iris-virginica
36.53.25.12.0Iris-virginica
44.92.54.51.7Iris-virginica
56.02.75.11.6Iris-versicolor
\n", + "
" + ], + "text/plain": [ + " sl sw pl pw Gatunek\n", + "0 5.2 3.4 1.4 0.2 Iris-setosa\n", + "1 5.1 3.7 1.5 0.4 Iris-setosa\n", + "2 6.7 3.1 5.6 2.4 Iris-virginica\n", + "3 6.5 3.2 5.1 2.0 Iris-virginica\n", + "4 4.9 2.5 4.5 1.7 Iris-virginica\n", + "5 6.0 2.7 5.1 1.6 Iris-versicolor" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas\n", + "data_iris = pandas.read_csv('iris.csv')\n", + "data_iris[:6]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Przygotowanie danych" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('X = ', matrix([[ 1. , 5.2, 3.4, 1.4, 0.2],\n", + " [ 1. , 5.1, 3.7, 1.5, 0.4],\n", + " [ 1. , 6.7, 3.1, 5.6, 2.4],\n", + " [ 1. , 6.5, 3.2, 5.1, 2. ]]))\n", + "('y = ', matrix([['Iris-setosa'],\n", + " ['Iris-setosa'],\n", + " ['Iris-virginica'],\n", + " ['Iris-virginica']], dtype=object))\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "\n", + "features = ['sl', 'sw', 'pl', 'pw']\n", + "m = len(data_iris)\n", + "X = np.matrix(data_iris[features])\n", + "X0 = np.ones(m).reshape(m, 1)\n", + "X = np.hstack((X0, X))\n", + "y = np.matrix(data_iris[[\"Gatunek\"]]).reshape(m, 1)\n", + "\n", + "print(\"X = \", X[:4])\n", + "print(\"y = \", y[:4])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Zamieńmy etykiety tekstowe w tablicy $y$ na wektory jednostkowe (_one-hot vectors_):\n", + "\n", + "$$\n", + "\\begin{array}{ccc}\n", + "\\mbox{\"Iris-setosa\"} & \\mapsto & \\left[ \\begin{array}{ccc} 1 & 0 & 0 \\\\ \\end{array} \\right] \\\\\n", + "\\mbox{\"Iris-virginica\"} & \\mapsto & \\left[ \\begin{array}{ccc} 0 & 1 & 0 \\\\ \\end{array} \\right] \\\\\n", + "\\mbox{\"Iris-versicolor\"} & \\mapsto & \\left[ \\begin{array}{ccc} 0 & 0 & 1 \\\\ \\end{array} \\right] \\\\\n", + "\\end{array}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Wówczas zamiast wektora $y$ otrzymamy macierz $Y$:\n", + "\n", + "$$\n", + "y \\; = \\;\n", + "\\left[\n", + "\\begin{array}{c}\n", + "y^{(1)} \\\\\n", + "y^{(2)} \\\\\n", + "y^{(3)} \\\\\n", + "y^{(4)} \\\\\n", + "y^{(5)} \\\\\n", + "\\vdots \\\\\n", + "\\end{array}\n", + "\\right]\n", + "\\; = \\;\n", + "\\left[\n", + "\\begin{array}{c}\n", + "\\mbox{\"Iris-setosa\"} \\\\\n", + "\\mbox{\"Iris-setosa\"} \\\\\n", + "\\mbox{\"Iris-virginica\"} \\\\\n", + "\\mbox{\"Iris-versicolor\"} \\\\\n", + "\\mbox{\"Iris-virginica\"} \\\\\n", + "\\vdots \\\\\n", + "\\end{array}\n", + "\\right]\n", + "\\quad \\mapsto \\quad\n", + "Y \\; = \\;\n", + "\\left[\n", + "\\begin{array}{ccc}\n", + "1 & 0 & 0 \\\\\n", + "1 & 0 & 0 \\\\\n", + "0 & 1 & 0 \\\\\n", + "0 & 0 & 1 \\\\\n", + "0 & 1 & 0 \\\\\n", + "\\vdots & \\vdots & \\vdots \\\\\n", + "\\end{array}\n", + "\\right]\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def mapY(y, cls):\n", + " m = len(y)\n", + " yBi = np.matrix(np.zeros(m)).reshape(m, 1)\n", + " yBi[y == cls] = 1.\n", + " return yBi\n", + "\n", + "def indicatorMatrix(y):\n", + " classes = np.unique(y.tolist())\n", + " m = len(y)\n", + " k = len(classes)\n", + " Y = np.matrix(np.zeros((m, k)))\n", + " for i, cls in enumerate(classes):\n", + " Y[:, i] = mapY(y, cls)\n", + " return Y\n", + "\n", + "# one-hot matrix\n", + "Y = indicatorMatrix(y)" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Podział danych na zbiór trenujący i testowy\n", + "XTrain, XTest = X[:100], X[100:]\n", + "YTrain, YTest = Y[:100], Y[100:]\n", + "\n", + "# Macierz parametrów początkowych\n", + "thetaTemp = np.ones(5).reshape(5,1)" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/svg+xml": [ + "\n", + "\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " 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\n", + "\n" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "g = seaborn.pairplot(data_iris, hue='Gatunek', size=1.75, aspect=1.5) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Od regresji logistycznej dwuklasowej do wieloklasowej\n", + "\n", + "* Irysy są przydzielone do trzech klas: _Iris-setosa_ (0), _Iris-versicolor_ (1), _Iris-virginica_ (2).\n", + "* Wiemy, jak stworzyć klasyfikatory typu _Iris-setosa_ vs. _Nie-Iris-setosa_ (tzw. _one-vs-all_).\n", + "* Możemy stworzyć trzy klasyfikatory $h_{\\theta_1}, h_{\\theta_2}, h_{\\theta_3}$ (otrzymując trzy zestawy parametrów $\\theta$) i wybrać klasę o najwyższym prawdopodobieństwie." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Funkcja _softmax_\n", + "\n", + "Odpowiednikiem funkcji logistycznej dla wieloklasowej regresji logistycznej jest funkcja $\\mathrm{softmax}$:\n", + "\n", + "$$ \\textrm{softmax}(k,x_1,\\dots,x_n) = \\dfrac{e^{x_k}}{\\sum_{i=i}^{n}e^{x_i}} $$\n", + "\n", + "$$P(y=c|x;\\theta_1,\\ldots,\\theta_k) = \\textrm{softmax}(c,\\theta_1^Tx,\\ldots,\\theta_k^Tx)$$" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('X5 =', matrix([[ 1. , 5.2, 3.4, 1.4, 0.2],\n", + " [ 1. , 5.1, 3.7, 1.5, 0.4],\n", + " [ 1. , 6.7, 3.1, 5.6, 2.4]]))\n", + "('softmax =', matrix([[ 0.00175241, 0.11686208, 0.01931717, 0.0026143 , 0.00078741],\n", + " [ 0.00175241, 0.10574119, 0.02607546, 0.00288924, 0.00096175],\n", + " [ 0.00175241, 0.52373952, 0.01431051, 0.17433774, 0.00710639]]))\n" + ] + } + ], + "source": [ + "# Zapis macierzowy funkcji softmax\n", + "def softmax(X):\n", + " return np.exp(X) / np.sum(np.exp(X))\n", + "\n", + "X5 = X[:3]\n", + "print(\"X5 =\", X5)\n", + "print(\"softmax =\", softmax(X5))" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 2.1]\n", + " [ 0.5]\n", + " [ 0.8]\n", + " [ 0.9]\n", + " [ 3.2]]\n", + "('Suma X =', 7.5000000000000009, '\\n')\n", + "[[ 0.20921428]\n", + " [ 0.04223963]\n", + " [ 0.05701754]\n", + " [ 0.06301413]\n", + " [ 0.62851442]]\n", + "('Suma P =', 0.99999999999999989)\n" + ] + } + ], + "source": [ + "XN = np.matrix([2.1, 0.5, 0.8, 0.9, 3.2]).reshape(5,1)\n", + "P = softmax(XN)\n", + "print(XN)\n", + "print(\"Suma X =\", np.sum(XN), \"\\n\")\n", + "print(P)\n", + "print(\"Suma P =\", np.sum(P)) " + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(matrix([[ 0.5672792 ],\n", + " [ 0.34410521],\n", + " [ 1.21453693],\n", + " [-2.06603751],\n", + " [-0.71099741]]), '\\n')\n", + "(matrix([[ 0.40938528],\n", + " [ 0.07134866],\n", + " [-0.93345289],\n", + " [ 0.62108863],\n", + " [-0.8021439 ]]), '\\n')\n", + "(matrix([[-0.13931903],\n", + " [-1.53046299],\n", + " [-2.02411945],\n", + " [ 2.24311323],\n", + " [ 2.75874817]]), '\\n')\n" + ] + } + ], + "source": [ + "def trainMaxEnt(X, Y):\n", + " n = X.shape[1]\n", + " thetas = []\n", + " for c in range(Y.shape[1]):\n", + " YBi = Y[:,c]\n", + " theta = np.matrix(np.random.random(n)).reshape(n,1)\n", + " thetaBest, errors = GD(h, J, dJ, theta, \n", + " X, YBi, alpha=0.1, eps=10**-4)\n", + " thetas.append(thetaBest)\n", + " return thetas\n", + "\n", + "thetas = trainMaxEnt(XTrain, YTrain);\n", + "for theta in thetas:\n", + " print(theta, \"\\n\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Funkcja decyzyjna wieloklasowej regresji logistycznej\n", + "\n", + "$$ c = \\mathop{\\textrm{arg}\\,\\textrm{max}}_{i \\in \\{1, \\ldots ,k\\}} P(y=i|x;\\theta_1,\\ldots,\\theta_k) $$" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('YTest =', matrix([[ 0., 0., 1.],\n", + " [ 1., 0., 0.],\n", + " [ 0., 0., 1.],\n", + " [ 0., 0., 1.],\n", + " [ 0., 0., 1.],\n", + " [ 1., 0., 0.]]))\n", + "('YTestCls =', matrix([[ 2.],\n", + " [ 0.],\n", + " [ 2.],\n", + " [ 2.],\n", + " [ 2.],\n", + " [ 0.]]), '\\n')\n" + ] + } + ], + "source": [ + "def classify(thetas, X, debug=False):\n", + " regs = np.array([(X*theta).item() for theta in thetas])\n", + " if debug:\n", + " print(\"regs =\", regs)\n", + " probs = softmax(regs)\n", + " if debug:\n", + " print(\"probs =\", np.around(probs,decimals=3))\n", + " return np.argmax(probs), probs\n", + "\n", + "print(\"YTest =\", YTest[:6])\n", + "YTestCls = YTest * np.matrix((0,1,2)).T\n", + "print(\"YTestCls =\", YTestCls[:6], \"\\n\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Ewaluacja" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "('regs =', array([-7.69442729, 0.69221651, 1.91571479]))\n", + "('probs =', array([ 0. , 0.227, 0.773]))\n", + "(2, ' <=>', 2, ' -- ', True, [0.0001, 0.2273, 0.7726])\n", + "('regs =', array([ 2.75684328, -1.41961889, -9.58991675]))\n", + "('probs =', array([ 0.985, 0.015, 0. ]))\n", + "(0, ' <=>', 0, ' -- ', True, [0.9849, 0.0151, 0.0])\n", + "('regs =', array([-7.02867886, 0.09552286, 1.9497746 ]))\n", + "('probs =', array([ 0. , 0.135, 0.865]))\n", + "(2, ' <=>', 2, ' -- ', True, [0.0001, 0.1354, 0.8645])\n", + "('regs =', array([-5.57547589, -0.24632327, 1.16421515]))\n", + "('probs =', array([ 0.001, 0.196, 0.803]))\n", + "(2, ' <=>', 2, ' -- ', True, [0.001, 0.196, 0.8031])\n", + "('regs =', array([-6.74108941, 0.77272949, 1.68582768]))\n", + "('probs =', array([ 0. , 0.286, 0.714]))\n", + "(2, ' <=>', 2, ' -- ', True, [0.0002, 0.2863, 0.7135])\n", + "('regs =', array([ 3.36547865, -2.11080509, -11.38109326]))\n", + "('probs =', array([ 0.996, 0.004, 0. ]))\n", + "(0, ' <=>', 0, ' -- ', True, [0.9958, 0.0042, 0.0])\n", + "('\\nAccuracy =', 1.0)\n" + ] + } + ], + "source": [ + "acc = 0.0\n", + "for i in range(len(YTestCls)):\n", + " cls, probs = classify(thetas, XTest[i], i < 6)\n", + " correctCls = int(YTestCls[i].item())\n", + " if i < 6:\n", + " print(correctCls, \" <=>\", cls, \" -- \", cls == correctCls, np.round(probs, 4).tolist())\n", + " acc += correctCls == cls\n", + "print(\"\\nAccuracy =\", acc/len(XTest))" + ] + } + ], + "metadata": { + "celltoolbar": "Slideshow", 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Regresja logistyczna\n", + "### Część 2" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 2.5. Regresja wielomianowa" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Wybór cech" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Zadanie: przewidzieć cenę działki o kształcie prostokąta.\n", + "\n", + "Jakie cechy wybrać?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + " * $x_1$ – szerokość działki, $x_2$ – długość działki:\n", + "$$ h_{\\theta}(\\vec{x}) = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + " * $x_1$ – powierzchnia działki:\n", + "$$ h_{\\theta}(\\vec{x}) = \\theta_0 + \\theta_1 x_1 $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Regresja wielomianowa" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przydtne importy\n", + "\n", + "import ipywidgets as widgets\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas\n", + "\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przydatne funkcje\n", + "\n", + "# Wersja macierzowa funkcji kosztu\n", + "def cost(theta, X, y):\n", + " m = len(y)\n", + " J = 1.0 / (2.0 * m) * ((X * theta - y).T * (X * theta - y))\n", + " return J.item()\n", + "\n", + "# Wersja macierzowa gradientu funkcji kosztu\n", + "def gradient(theta, X, y):\n", + " return 1.0 / len(y) * (X.T * (X * theta - y)) \n", + "\n", + "# Algorytm gradientu prostego (wersja macierzowa)\n", + "def gradient_descent(fJ, fdJ, theta, X, y, alpha=0.1, eps=10**-5):\n", + " current_cost = fJ(theta, X, y)\n", + " logs = [[current_cost, theta]]\n", + " while True:\n", + " theta = theta - alpha * fdJ(theta, X, y)\n", + " current_cost, prev_cost = fJ(theta, X, y), current_cost\n", + " if abs(prev_cost - current_cost) > 10**15:\n", + " print('Algorithm does not converge!')\n", + " break\n", + " if abs(prev_cost - current_cost) <= eps:\n", + " break\n", + " logs.append([current_cost, theta]) \n", + " return theta, logs\n", + "\n", + "# Wykres danych (wersja macierzowa)\n", + "def plot_data(X, y, xlabel, ylabel): \n", + " fig = plt.figure(figsize=(16*.6, 9*.6))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + " ax.scatter([X[:, 1]], [y], c='r', s=50, label='Dane')\n", + " \n", + " ax.set_xlabel(xlabel)\n", + " ax.set_ylabel(ylabel)\n", + " ax.margins(.05, .05)\n", + " plt.ylim(y.min() - 1, y.max() + 1)\n", + " plt.xlim(np.min(X[:, 1]) - 1, np.max(X[:, 1]) + 1)\n", + " return fig\n", + "\n", + "# Wykres funkcji fun\n", + "def plot_fun(fig, fun, X):\n", + " ax = fig.axes[0]\n", + " x0 = np.min(X[:, 1]) - 1.0\n", + " x1 = np.max(X[:, 1]) + 1.0\n", + " Arg = np.arange(x0, x1, 0.1)\n", + " Val = fun(Arg)\n", + " return ax.plot(Arg, Val, linewidth='2')" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wczytanie danych (mieszkania) przy pomocy biblioteki pandas\n", + "\n", + "alldata = pandas.read_csv('data_flats.tsv', header=0, sep='\\t',\n", + " usecols=['price', 'rooms', 'sqrMetres'])\n", + "data = np.matrix(alldata[['sqrMetres', 'price']])\n", + "\n", + "m, n_plus_1 = data.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data[:, 0:n]\n", + "Xn /= np.amax(Xn, axis=0)\n", + "Xn2 = np.power(Xn, 2) \n", + "Xn2 /= np.amax(Xn2, axis=0)\n", + "Xn3 = np.power(Xn, 3) \n", + "Xn3 /= np.amax(Xn3, axis=0)\n", + "\n", + "X = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n + 1)\n", + "X2 = np.matrix(np.concatenate((np.ones((m, 1)), Xn, Xn2), axis=1)).reshape(m, 2 * n + 1)\n", + "X3 = np.matrix(np.concatenate((np.ones((m, 1)), Xn, Xn2, Xn3), axis=1)).reshape(m, 3 * n + 1)\n", + "y = np.matrix(data[:, -1]).reshape(m, 1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Postać ogólna regresji wielomianowej:\n", + "\n", + "$$ h_{\\theta}(x) = \\sum_{i=1}^{n} \\theta_i x^i $$" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [], + "source": [ + "# Funkcja regresji wielomianowej\n", + "\n", + "def h_poly(Theta, x):\n", + " return sum(theta * np.power(x, i) for i, theta in enumerate(Theta.tolist()))\n", + "\n", + "def polynomial_regression(theta):\n", + " return lambda x: h_poly(theta, x)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Funkcja kwadratowa:\n", + "\n", + "$$ h_{\\theta}(x) = \\theta_0 + \\theta_1 x + \\theta_2 x^2 $$" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 54, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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11n4N5AOj/B/51tqN1toy4DlgonH+uXca8KL//bOBSdWuNdv/+YvA6f7zg91D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\ncK8/e3bzvXLBydH06bBvn1c+5bbb4Je/9IbBg+c8hiqZk5t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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data(X2, y, xlabel='x', ylabel='y')\n", + "theta_start = np.matrix([0, 0, 0]).reshape(3, 1)\n", + "theta, logs = gradient_descent(cost, gradient, theta_start, X2, y)\n", + "plot_fun(fig, polynomial_regression(theta), X)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Funkcja sześcienna:\n", + "\n", + "$$ h_{\\theta}(x) = \\theta_0 + \\theta_1 x + \\theta_2 x^2 + \\theta_3 x^3 $$" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 397519.38046962]\n", + " [ -841341.14146733]\n", + " [ 2253713.97125102]\n", + " [ -244009.07081946]]\n" + ] + }, + { + "data": { + "image/png": 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YYxKMMQnA48C5wGDgCt+5AH/xXasfsB/wl5xNBfb7xh/ynRfwHiH+Pce160/q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\nGdmzDXsKynj0Y+0TLBJuXq/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ZZm7oknTXrvD447Wf//jj0Llz0+ILJC3NmVWs7RnF3Fx4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\nq3LBydFVV8HevV77lOnT4Xe/84bBg695DNUyJyfn2EQx3jp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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data(X3, y, xlabel='x', ylabel='y')\n", + "theta_start = np.matrix([0, 0, 0, 0]).reshape(4, 1)\n", + "theta, _ = gradient_descent(cost, gradient, theta_start, X3, y)\n", + "plot_fun(fig, polynomial_regression(theta), X)\n", + "\n", + "print(theta)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Regresję wielomianową można potraktować jako szczególny przypadek regresji liniowej wielu zmiennych:\n", + "\n", + "$$ h_{\\theta}(x) = \\theta_0 + \\theta_1 x + \\theta_2 x^2 + \\theta_3 x^3 $$\n", + "$$ x_1 = x, \\quad x_2 = x^2, \\quad x_3 = x^3, \\quad \\vec{x} = \\left[ \\begin{array}{ccc} x_0 \\\\ x_1 \\\\ x_2 \\end{array} \\right] $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Uwaga praktyczna: przyda się normalizacja cech, szczególnie skalowanie!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "W ten sposób możemy stosować również inne „pochodne” cechy, np.:\n", + "\n", + "$$ h_{\\theta}(x) = \\theta_0 + \\theta_1 x + \\theta_2 \\sqrt{x} $$\n", + "$$ x_1 = x, \\quad x_2 = \\sqrt{x}, \\quad \\vec{x} = \\left[ \\begin{array}{ccc} x_0 \\\\ x_1 \\end{array} \\right] $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Wielomianowa regresja logistyczna\n", + "\n", + "Podobne modyfikacje cech możemy również stosować dla regresji logistycznej." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def powerme(x1,x2,n):\n", + " X = []\n", + " for m in range(n+1):\n", + " for i in range(m+1):\n", + " X.append(np.multiply(np.power(x1,i),np.power(x2,(m-i))))\n", + " return np.hstack(X)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "matrix([[ 1. , 0.36596696, -0.11214686],\n", + " [ 0. , 0.4945305 , 0.47110656],\n", + " [ 0. , 0.70290604, -0.92257983],\n", + " [ 0. , 0.46658862, -0.62269739],\n", + " [ 0. , 0.87939462, -0.11408015],\n", + " [ 0. , -0.331185 , 0.84447667],\n", + " [ 0. , -0.54351701, 0.8851383 ],\n", + " [ 0. , 0.91979241, 0.41607012],\n", + " [ 0. , 0.28011742, 0.61431157],\n", + " [ 0. , 0.94754363, -0.78307311]])" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Wczytanie danych\n", + "import pandas\n", + "import numpy as np\n", + "\n", + "alldata = pandas.read_csv('polynomial_logistic.tsv', sep='\\t')\n", + "data = np.matrix(alldata)\n", + "\n", + "m, n_plus_1 = data.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data[:, 1:]\n", + "\n", + "Xpl = powerme(data[:, 1], data[:, 2], n)\n", + "Ypl = np.matrix(data[:, 0]).reshape(m, 1)\n", + "\n", + "data[:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wykres danych (wersja macierzowa)\n", + "def plot_data_for_classification(X, Y, xlabel, ylabel): \n", + " fig = plt.figure(figsize=(16*.6, 9*.6))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + " X = X.tolist()\n", + " Y = Y.tolist()\n", + " X1n = [x[1] for x, y in zip(X, Y) if y[0] == 0]\n", + " X1p = [x[1] for x, y in zip(X, Y) if y[0] == 1]\n", + " X2n = [x[2] for x, y in zip(X, Y) if y[0] == 0]\n", + " X2p = [x[2] for x, y in zip(X, Y) if y[0] == 1]\n", + " ax.scatter(X1n, X2n, c='r', marker='x', s=50, label='Dane')\n", + " ax.scatter(X1p, X2p, c='g', marker='o', s=50, label='Dane')\n", + " \n", + " ax.set_xlabel(xlabel)\n", + " ax.set_ylabel(ylabel)\n", + " ax.margins(.05, .05)\n", + " return fig" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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TqQEFcQxiANAz6R+25Adt9tysamej6WfOnsm5hcDqUZQ5IIcOLQzeknItycAG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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(Xpl, Ypl, xlabel=r'$x_1$', ylabel=r'$x_2$')" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Propozycja hipotezy:\n", + "\n", + "$$ h_\\theta(x) = g(\\theta^T x) = g(\\theta_0 + \\theta_1 x_1 + \\theta_2 x_2 + \\theta_3 x_3 + \\theta_4 x_4 + \\theta_5 x_5) \\; , $$\n", + "\n", + "gdzie $g$ – funkcja logistyczna, $x_3 = x_1^2$, $x_4 = x_2^2$, $x_5 = x_1 x_2$." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def safeSigmoid(x, eps=0):\n", + " y = 1.0/(1.0 + np.exp(-x))\n", + " if eps > 0:\n", + " y[y < eps] = eps\n", + " y[y > 1 - eps] = 1 - eps\n", + " return y\n", + "\n", + "def h(theta, X, eps=0.0):\n", + " return safeSigmoid(X*theta, eps)\n", + "\n", + "def J(h,theta,X,y, lamb=0):\n", + " m = len(y)\n", + " f = h(theta, X, eps=10**-7)\n", + " j = -np.sum(np.multiply(y, np.log(f)) + \n", + " np.multiply(1 - y, np.log(1 - f)), axis=0)/m\n", + " if lamb > 0:\n", + " j += lamb/(2*m) * np.sum(np.power(theta[1:],2))\n", + " return j\n", + "\n", + "def dJ(h,theta,X,y,lamb=0):\n", + " g = 1.0/y.shape[0]*(X.T*(h(theta,X)-y))\n", + " if lamb > 0:\n", + " g[1:] += lamb/float(y.shape[0]) * theta[1:] \n", + " return g\n", + "\n", + "def classifyBi(theta, X):\n", + " prob = h(theta, X)\n", + " return prob" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Metoda gradientu prostego dla regresji logistycznej\n", + "def GD(h, fJ, fdJ, theta, X, y, alpha=0.01, eps=10**-3, maxSteps=10000):\n", + " errorCurr = fJ(h, theta, X, y)\n", + " errors = [[errorCurr, theta]]\n", + " while True:\n", + " # oblicz nowe theta\n", + " theta = theta - alpha * fdJ(h, theta, X, y)\n", + " # raportuj poziom błędu\n", + " errorCurr, errorPrev = fJ(h, theta, X, y), errorCurr\n", + " # kryteria stopu\n", + " if abs(errorPrev - errorCurr) <= eps:\n", + " break\n", + " if len(errors) > maxSteps:\n", + " break\n", + " errors.append([errorCurr, theta]) \n", + " return theta, errors" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = [[ 1.59558981]\n", + " [ 0.12602307]\n", + " [ 0.65718518]\n", + " [-5.26367581]\n", + " [ 1.96832544]\n", + " [-6.97946065]]\n" + ] + } + ], + "source": [ + "# Uruchomienie metody gradientu prostego dla regresji logistycznej\n", + "theta_start = np.matrix(np.zeros(Xpl.shape[1])).reshape(Xpl.shape[1],1)\n", + "theta, errors = GD(h, J, dJ, theta_start, Xpl, Ypl, \n", + " alpha=0.1, eps=10**-7, maxSteps=10000)\n", + "print(r'theta = {}'.format(theta))" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wykres granicy klas\n", + "def plot_decision_boundary(fig, theta, X):\n", + " ax = fig.axes[0]\n", + " xx, yy = np.meshgrid(np.arange(-1.0, 1.0, 0.02),\n", + " np.arange(-1.0, 1.0, 0.02))\n", + " l = len(xx.ravel())\n", + " C = powerme(xx.reshape(l, 1), yy.reshape(l, 1), n)\n", + " z = classifyBi(theta, C).reshape(int(np.sqrt(l)), int(np.sqrt(l)))\n", + "\n", + " plt.contour(xx, yy, z, levels=[0.5], lw=3);" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/pawel/.local/lib/python2.7/site-packages/matplotlib/contour.py:967: UserWarning: The following kwargs were not used by contour: 'lw'\n", + " s)\n" + ] + }, + { + "data": { + "image/png": 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xpuAM3lj8LJM3Ih/9c+p9CI8Ix9sjP0AoNn6QvjCBIzKS8ibG9iGJ27IyG49e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\n8MpdiIyK1Dq0ypk1y16n7HpOdp6zBw2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HZl4HvJ/qejhJmjuvgZOkNYqIDcAH\ngecAF2bmh1qukqQFZwInSZLUM55ClSRJ6hkTOEmSpJ4xgZMkSeoZEzhJkqSeMYGTJEnqGRM4SZKk\nnjGBkyRJ6hkTOEmSpJ75H6zqsn7OT0cUAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(Xpl, Ypl, xlabel=r'$x_1$', ylabel=r'$x_2$')\n", + "plot_decision_boundary(fig, theta, Xpl)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wczytanie danych\n", + "\n", + "alldata = pandas.read_csv('polynomial_logistic.tsv', sep='\\t')\n", + "data = np.matrix(alldata)\n", + "\n", + "m, n_plus_1 = data.shape\n", + "Xn = data[:, 1:]\n", + "\n", + "n = 10\n", + "Xpl = powerme(data[:, 1], data[:, 2], n)\n", + "Ypl = np.matrix(data[:, 0]).reshape(m, 1)\n", + "\n", + "theta_start = np.matrix(np.zeros(Xpl.shape[1])).reshape(Xpl.shape[1],1)\n", + "theta, errors = GD(h, J, dJ, theta_start, Xpl, Ypl, \n", + " alpha=0.1, eps=10**-7, maxSteps=10000)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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Od7ouPDgcbev7cCuOjwkKDsKND/fHJ9vn4NbHb8KSz//E/ReOwYK3foa5xKx1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\n4awjsuL71fLxM1/JpAEvnh7qwz4m37Q74+XnuUs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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Przykład dla większej liczby cech\n", + "fig = plot_data_for_classification(Xpl, Ypl, xlabel=r'$x_1$', ylabel=r'$x_2$')\n", + "plot_decision_boundary(fig, theta, Xpl)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 2.6. Problem nadmiernego dopasowania" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Obciążenie a wariancja" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Dane do prostego przykładu\n", + "\n", + "data = np.matrix([\n", + " [0.0, 0.0],\n", + " [0.5, 1.8],\n", + " [1.0, 4.8],\n", + " [1.6, 7.2],\n", + " [2.6, 8.8],\n", + " [3.0, 9.0],\n", + " ])\n", + "\n", + "m, n_plus_1 = data.shape\n", + "n = n_plus_1 - 1\n", + "Xn1 = data[:, 0:n]\n", + "Xn1 /= np.amax(Xn1, axis=0)\n", + "Xn2 = np.power(Xn1, 2) \n", + "Xn2 /= np.amax(Xn2, axis=0)\n", + "Xn3 = np.power(Xn1, 3) \n", + "Xn3 /= np.amax(Xn3, axis=0)\n", + "Xn4 = np.power(Xn1, 4) \n", + "Xn4 /= np.amax(Xn4, axis=0)\n", + "Xn5 = np.power(Xn1, 5) \n", + "Xn5 /= np.amax(Xn5, axis=0)\n", + "\n", + "X1 = np.matrix(np.concatenate((np.ones((m, 1)), Xn1), axis=1)).reshape(m, n + 1)\n", + "X2 = np.matrix(np.concatenate((np.ones((m, 1)), Xn1, Xn2), axis=1)).reshape(m, 2 * n + 1)\n", + "X5 = np.matrix(np.concatenate((np.ones((m, 1)), Xn1, Xn2, Xn3, Xn4, Xn5), axis=1)).reshape(m, 5 * n + 1)\n", + "y = np.matrix(data[:, -1]).reshape(m, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data(X1, y, xlabel='x', ylabel='y')" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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9st+RACAuUcCAOFF5qF7XF5fKOelH5w3RaQM7+x0JAOIWBQyIA8453frMUu2o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\nVwaap7tzbkfT5zsldT/O49L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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data(X1, y, xlabel='x', ylabel='y')\n", + "theta_start = np.matrix([0, 0]).reshape(2, 1)\n", + "theta, _ = gradient_descent(cost, gradient, theta_start, X1, y, eps=0.00001)\n", + "plot_fun(fig, polynomial_regression(theta), X1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Ten model ma duże **obciążenie** (**błąd systematyczny**, _bias_) – zachodzi **niedostateczne dopasowanie** (_underfitting_)." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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GHyXGseUQEI1+eVpvpSbEasaqUn26utR1nBZHAQPg1JOzi7S1vFrHdG6tcwd1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\nAADgsf8PQ5GyUdomDXUAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data(X2, y, xlabel='x', ylabel='y')\n", + "theta_start = np.matrix([0, 0, 0]).reshape(3, 1)\n", + "theta, _ = gradient_descent(cost, gradient, theta_start, X2, y, eps=0.000001)\n", + "plot_fun(fig, polynomial_regression(theta), X1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Ten model jest odpowiednio dopasowany." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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AGWP6SxojabHLHEA0WbSlVGt3Vqhrcry+NYbffQDABWcFzBiTIuk5SbOstRX7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\nmIB/QNmZqfrlN4+SJP38+dU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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data(X5, y, xlabel='x', ylabel='y')\n", + "theta_start = np.matrix([0, 0, 0, 0, 0, 0]).reshape(6, 1)\n", + "theta, _ = gradient_descent(cost, gradient, theta_start, X5, y, alpha=0.5, eps=10**-7)\n", + "plot_fun(fig, polynomial_regression(theta), X1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Ten model ma dużą **wariancję** (_variance_) – zachodzi **nadmierne dopasowanie** (_overfitting_)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Obciążenie (błąd systematyczny, _bias_)\n", + "\n", + "* Wynika z błędnych założeń co do algorytmu uczącego się.\n", + "* Duże obciążenie powoduje niedostateczne dopasowanie." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Wariancja (_variance_)\n", + "\n", + "* Wynika z nadwrażliwości na niewielkie fluktuacje w zbiorze uczącym.\n", + "* Wysoka wariancja może spowodować nadmierne dopasowanie (modelując szum zamiast sygnału)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 2.7. Metodologia testowania" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Zbiór uczący a zbiór testowy" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Na zbiorze uczącym (treningowym) uczymy algorytmy, a na zbiorze testowym sprawdzamy ich poprawność.\n", + "* Zbiór uczący powinien być kilkukrotnie większy od testowego (np. 4:1, 9:1 itp.).\n", + "* Zbiór testowy często jest nieznany.\n", + "* Należy unikać mieszania danych testowych i treningowych – nie wolno „zanieczyszczać” danych treningowych danymi testowymi!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Czasami potrzebujemy dobrać parametry modelu, np. $\\alpha$ – który zbiór wykorzystać do tego celu?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true, + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Zbiór walidacyjny" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Do doboru parametrów najlepiej użyć jeszcze innego zbioru – jest to tzw. **zbiór walidacyjny**" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + " * Zbiór walidacyjny powinien mieć wielkość zbliżoną do wielkości zbioru testowego, czyli np. dane można podzielić na te trzy zbiory w proporcjach 3:1:1, 8:1:1 itp." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Walidacja krzyżowa" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Którą część danych wydzielić jako zbiór walidacyjny tak, żeby było „najlepiej”?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + " * Niech każda partia danych pełni tę rolę naprzemiennie!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\n", + "Żródło: https://chrisjmccormick.wordpress.com/2013/07/31/k-fold-cross-validation-with-matlab-code/" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Walidacja krzyżowa\n", + "\n", + "* Podziel dane $D = \\left\\{ (x^{(1)}, y^{(1)}), \\ldots, (x^{(m)}, y^{(m)})\\right\\} $ na $N$ rozłącznych zbiorów $T_1,\\ldots,T_N$\n", + "* Dla $i=1,\\ldots,N$, wykonaj:\n", + " * Użyj $T_i$ do walidacji i zbiór $S_i$ do trenowania, gdzie $S_i = D \\smallsetminus T_i$. \n", + " * Zapisz model $\\theta_i$.\n", + "* Akumuluj wyniki dla modeli $\\theta_i$ dla zbiorów $T_i$.\n", + "* Ustalaj parametry uczenia na akumulowanych wynikach." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Walidacja krzyżowa – wskazówki\n", + "\n", + "* Zazwyczaj ustala się $N$ w przedziale od $4$ do $10$, tzw. $N$-krotna walidacja krzyżowa (_$N$-fold cross validation_). \n", + "* Zbiór $D$ warto zrandomizować przed podziałem.\n", + "* W jaki sposób akumulować wyniki dla wszystkich zbiórow $T_i$?\n", + "* Po ustaleniu parametrów dla każdego $T_i$, trenujemy model na całych danych treningowych z ustalonymi parametrami.\n", + "* Testujemy na zbiorze testowym (jeśli nim dysponujemy)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### _Leave-one-out_\n", + "\n", + "Jest to szczególny przypadek walidacji krzyżowej, w której $N = m$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Jaki jest rozmiar pojedynczego zbioru $T_i$?\n", + "* Jakie są zalety i wady tej metody?\n", + "* Kiedy może być przydatna?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Zbiór walidujący a algorytmy optymalizacji\n", + "\n", + "* Gdy błąd rośnie na zbiorze uczącym, mamy źle dobrany parametr $\\alpha$. Należy go wtedy zmniejszyć.\n", + "* Gdy błąd zmniejsza się na zbiorze trenującym, ale rośnie na zbiorze walidującym, mamy do czynienia ze zjawiskiem **nadmiernego dopasowania** (_overfitting_).\n", + "* Należy wtedy przerwać optymalizację. Automatyzacja tego procesu to _early stopping_." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 2.8. Regularyzacja" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def SGD(h, fJ, fdJ, theta, X, Y, \n", + " alpha=0.001, maxEpochs=1.0, batchSize=100, \n", + " adaGrad=False, logError=False, validate=0.0, valStep=100, lamb=0, trainsetsize=1.0):\n", + " errorsX, errorsY = [], []\n", + " errorsVX, errorsVY = [], []\n", + " \n", + " XT, YT = X, Y\n", + " \n", + " m_end=int(trainsetsize*len(X))\n", + " \n", + " if validate > 0:\n", + " mv = int(X.shape[0] * validate)\n", + " XV, YV = X[:mv], Y[:mv] \n", + " XT, YT = X[mv:m_end], Y[mv:m_end] \n", + " m, n = XT.shape\n", + "\n", + " start, end = 0, batchSize\n", + " maxSteps = (m * float(maxEpochs)) / batchSize\n", + " \n", + " if adaGrad:\n", + " hgrad = np.matrix(np.zeros(n)).reshape(n,1)\n", + " \n", + " for i in range(int(maxSteps)):\n", + " XBatch, YBatch = XT[start:end,:], YT[start:end,:]\n", + "\n", + " grad = fdJ(h, theta, XBatch, YBatch, lamb=lamb)\n", + " if adaGrad:\n", + " hgrad += np.multiply(grad, grad)\n", + " Gt = 1.0 / (10**-7 + np.sqrt(hgrad))\n", + " theta = theta - np.multiply(alpha * Gt, grad)\n", + " else:\n", + " theta = theta - alpha * grad\n", + " \n", + " if logError:\n", + " errorsX.append(float(i*batchSize)/m)\n", + " errorsY.append(fJ(h, theta, XBatch, YBatch).item())\n", + " if validate > 0 and i % valStep == 0:\n", + " errorsVX.append(float(i*batchSize)/m)\n", + " errorsVY.append(fJ(h, theta, XV, YV).item())\n", + " \n", + " if start + batchSize < m:\n", + " start += batchSize\n", + " else:\n", + " start = 0\n", + " end = min(start + batchSize, m)\n", + " return theta, (errorsX, errorsY, errorsVX, errorsVY)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przygotowanie danych do przykładu regularyzacji\n", + "\n", + "n = 6\n", + "\n", + "data = np.matrix(np.loadtxt(\"ex2data2.txt\", delimiter=\",\"))\n", + "np.random.shuffle(data)\n", + "\n", + "X = powerme(data[:,0], data[:,1], n)\n", + "Y = data[:,2]" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def draw_regularization_example(X, Y, lamb=0, alpha=1, adaGrad=True, maxEpochs=2500, validate=0.25):\n", + " plt.figure(figsize=(16,8))\n", + " plt.subplot(121)\n", + " plt.scatter(X[:, 2].tolist(), X[:, 1].tolist(),\n", + " c=Y.tolist(),\n", + " s=100, cmap=plt.cm.get_cmap('prism'));\n", + "\n", + " theta = np.matrix(np.zeros(X.shape[1])).reshape(X.shape[1],1)\n", + " thetaBest, err = SGD(h, J, dJ, theta, X, Y, alpha=alpha, adaGrad=adaGrad, maxEpochs=maxEpochs, batchSize=100, \n", + " logError=True, validate=validate, valStep=1, lamb=lamb)\n", + "\n", + " xx, yy = np.meshgrid(np.arange(-1.5, 1.5, 0.02),\n", + " np.arange(-1.5, 1.5, 0.02))\n", + " l = len(xx.ravel())\n", + " C = powerme(xx.reshape(l, 1),yy.reshape(l, 1), n)\n", + " z = classifyBi(thetaBest, C).reshape(int(np.sqrt(l)), int(np.sqrt(l)))\n", + "\n", + " plt.contour(xx, yy, z, levels=[0.5], lw=3);\n", + " plt.ylim(-1,1.2);\n", + " plt.xlim(-1,1.2);\n", + " plt.legend();\n", + " plt.subplot(122)\n", + " plt.plot(err[0],err[1], lw=3, label=\"Training error\")\n", + " if validate > 0:\n", + " plt.plot(err[2],err[3], lw=3, label=\"Validation error\");\n", + " plt.legend()\n", + " plt.ylim(0.2,0.8);" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/pawel/.local/lib/python2.7/site-packages/ipykernel_launcher.py:2: RuntimeWarning: overflow encountered in exp\n", + " \n" + ] + }, + { + "data": { + "image/png": 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YuTJMnQobN2L6+LD8izVUvL8cpSoVT/sYTuCT14fRP43gkUFtWPzpMl5r9z4h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\nkYqkhFZEREREREQq0v8HnzlY4J8U7jwAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "draw_regularization_example(X, Y)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Regularyzacja\n", + "\n", + "* Metoda zapobiegania zjawisku nadmiernego dopasowania (*overfitting*)\n", + "* „Kara” za ekstremalne wartości parametrów $\\theta$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Regularyzacja dla regresji liniowej – funkcja kosztu\n", + "\n", + "$$\n", + "J(\\theta) \\, = \\, \\dfrac{1}{2m} \\left( \\displaystyle\\sum_{i=1}^{m} h_\\theta(x^{(i)}) - y^{(i)} \\color{red}{ + \\lambda \\displaystyle\\sum_{j=1}^{n} \\theta^2_j } \\right)\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* $\\lambda$ – parametr regularyzacji\n", + "* jeżeli $\\lambda$ jest zbyt mały, skutkuje to nadmiernym dopasowaniem\n", + "* jeżeli $\\lambda$ jest zbyt duży, skutkuje to niedostatecznym dopasowaniem" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Regularyzacja dla regresji liniowej – gradient\n", + "\n", + "$$\\small\n", + "\\begin{array}{llll}\n", + "\\dfrac{\\partial J(\\theta)}{\\partial \\theta_0} &=& \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_{\\theta}(x^{(i)})-y^{(i)} \\right) x^{(i)}_0 & \\textrm{dla $j = 0$ }\\\\\n", + "\\dfrac{\\partial J(\\theta)}{\\partial \\theta_j} &=& \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_{\\theta}(x^{(i)})-y^{(i)} \\right) x^{(i)}_j \\color{red}{+ \\dfrac{\\lambda}{m}\\theta_j} & \\textrm{dla $j = 1, 2, \\ldots, n $} \\\\\n", + "\\end{array} \n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Regularyzacja dla regresji logistycznej – funkcja kosztu\n", + "\n", + "$$\n", + "\\begin{array}{rtl}\n", + "J(\\theta) & = & -\\dfrac{1}{m} \\left( \\displaystyle\\sum_{i=1}^{m} y^{(i)} \\log h_\\theta(x^{(i)}) + \\left( 1-y^{(i)} \\right) \\log \\left( 1-h_\\theta(x^{(i)}) \\right) \\right) \\\\\n", + "& & \\color{red}{ + \\dfrac{\\lambda}{2m} \\displaystyle\\sum_{j=1}^{n} \\theta^2_j } \\\\\n", + "\\end{array}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Regularyzacja dla regresji logistycznej – gradient\n", + "\n", + "$$\\small\n", + "\\begin{array}{llll}\n", + "\\dfrac{\\partial J(\\theta)}{\\partial \\theta_0} &=& \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_{\\theta}(x^{(i)})-y^{(i)} \\right) x^{(i)}_0 & \\textrm{dla $j = 0$ }\\\\\n", + "\\dfrac{\\partial J(\\theta)}{\\partial \\theta_j} &=& \\dfrac{1}{m}\\displaystyle\\sum_{i=1}^m \\left( h_{\\theta}(x^{(i)})-y^{(i)} \\right) x^{(i)}_j \\color{red}{+ \\dfrac{\\lambda}{m}\\theta_j} & \\textrm{dla $j = 1, 2, \\ldots, n $} \\\\\n", + "\\end{array} \n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Implementacja metody regularyzacji" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "def J_(h,theta,X,y,lamb=0):\n", + " m = float(len(y))\n", + " f = h(theta, X, eps=10**-7)\n", + " j = 1.0/m \\\n", + " * -np.sum(np.multiply(y, np.log(f)) + \n", + " np.multiply(1 - y, np.log(1 - f)), axis=0) \\\n", + " + lamb/(2*m) * np.sum(np.power(theta[1:] ,2))\n", + " return j\n", + "\n", + "def dJ_(h,theta,X,y,lamb=0):\n", + " m = float(y.shape[0])\n", + " g = 1.0/y.shape[0]*(X.T*(h(theta,X)-y))\n", + " g[1:] += lamb/m * theta[1:]\n", + " return g" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "slider_lambda = widgets.FloatSlider(min=0.0, max=0.5, step=0.005, value=0.01, description=r'$\\lambda$', width=300)\n", + "\n", + "def slide_regularization_example_2(lamb):\n", + " draw_regularization_example(X, Y, lamb=lamb)" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "0738c69d0fff4e32ab23d4aa93ca9a71", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

Failed to display Jupyter Widget of type interactive.

\n", + "

\n", + " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", + " that the widgets JavaScript is still loading. If this message persists, it\n", + " likely means that the widgets JavaScript library is either not installed or\n", + " not enabled. See the Jupyter\n", + " Widgets Documentation for setup instructions.\n", + "

\n", + "

\n", + " If you're reading this message in another notebook frontend (for example, a static\n", + " rendering on GitHub or NBViewer),\n", + " it may mean that your frontend doesn't currently support widgets.\n", + "

\n" + ], + "text/plain": [ + "interactive(children=(FloatSlider(value=0.01, description=u'$\\\\lambda$', max=0.5, step=0.005), Button(description=u'Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "widgets.interact_manual(slide_regularization_example_2, lamb=slider_lambda)" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def cost_lambda_fun(lamb):\n", + " theta = np.matrix(np.zeros(X.shape[1])).reshape(X.shape[1],1)\n", + " thetaBest, err = SGD(h, J, dJ, theta, X, Y, alpha=1, adaGrad=True, maxEpochs=2500, batchSize=100, \n", + " logError=True, validate=0.25, valStep=1, lamb=lamb)\n", + " return err[1][-1], err[3][-1]\n", + "\n", + "def plot_cost_lambda():\n", + " plt.figure(figsize=(16,8))\n", + " ax = plt.subplot(111)\n", + " Lambda = np.arange(0.0, 1.0, 0.01)\n", + " Costs = [cost_lambda_fun(lamb) for lamb in Lambda]\n", + " CostTrain = [cost[0] for cost in Costs]\n", + " CostCV = [cost[1] for cost in Costs]\n", + " plt.plot(Lambda, CostTrain, lw=3, label='training error')\n", + " plt.plot(Lambda, CostCV, lw=3, label='validation error')\n", + " ax.set_xlabel(r'$\\lambda$')\n", + " ax.set_ylabel(u'cost')\n", + " plt.legend()\n", + " plt.ylim(0.2,0.8)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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a9QfDsUB1voZiYZoYqam8QVJRTmYsTEsLslWWEKpOrDrrZQXZzJ4CmHOIWQAA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\nnMusEma54d6EGdaEcG0/6DzqalKMVFT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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_cost_lambda()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 2.9. Krzywa uczenia się" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Krzywa uczenia pozwala sprawdzić, czy uczenie przebiega poprawnie.\n", + "* Krzywa uczenia to wykres zależności między wielkością zbioru treningowego a wartością funkcji kosztu.\n", + "* Wraz ze wzrostem wielkości zbioru treningowego wartość funkcji kosztu na zbiorze treningowym rośnie.\n", + "* Wraz ze wzrostem wielkości zbioru treningowego wartość funkcji kosztu na zbiorze walidacyjnym maleje." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def cost_trainsetsize_fun(m):\n", + " theta = np.matrix(np.zeros(X.shape[1])).reshape(X.shape[1],1)\n", + " thetaBest, err = SGD(h, J, dJ, theta, X, Y, alpha=1, adaGrad=True, maxEpochs=2500, batchSize=100, \n", + " logError=True, validate=0.25, valStep=1, lamb=0.01, trainsetsize=m)\n", + " return err[1][-1], err[3][-1]\n", + "\n", + "def plot_learning_curve():\n", + " plt.figure(figsize=(16,8))\n", + " ax = plt.subplot(111)\n", + " M = np.arange(0.3, 1.0, 0.05)\n", + " Costs = [cost_trainsetsize_fun(m) for m in M]\n", + " CostTrain = [cost[0] for cost in Costs]\n", + " CostCV = [cost[1] for cost in Costs]\n", + " plt.plot(M, CostTrain, lw=3, label='training error')\n", + " plt.plot(M, CostCV, lw=3, label='validation error')\n", + " ax.set_xlabel(u'trainset size')\n", + " ax.set_ylabel(u'cost')\n", + " plt.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Krzywa uczenia a obciążenie i wariancja\n", + "\n", + "\n", + "\n", + "Źródło: http://www.ritchieng.com/machinelearning-learning-curve" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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TvxVvHh263CZw1o8S85u/g51b4ssjSZIkVcEyq5qzan7lo3jn3w/ZOfHl0eHr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\nltNHctdZqo8VCXTWWgr317K2sJJ1RRWsLaxgTWElZdXt2ws3NNgwOjX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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_learning_curve()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 2.10. Obserwacje odstające" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Funkcja regresji liniowej\n", + "\n", + "def h_linear(Theta, x):\n", + " return x * Theta\n", + "\n", + "def linear_regression(theta):\n", + " return lambda x: h_linear(theta, x)\n", + "\n", + "# Wykres krzywej regresji (wersja macierzowa)\n", + "def plot_regression(fig, fun, theta, X):\n", + " ax = fig.axes[0]\n", + " x0 = np.min(X[:, 1]) - 1.0\n", + " x1 = np.max(X[:, 1]) + 1.0\n", + " L = [x0, x1]\n", + " LX = np.matrix([1, x0, 1, x1]).reshape(2, 2)\n", + " ax.plot(L, fun(theta, LX), linewidth='2',\n", + " label=(r'$y={theta0:.2}{op}{theta1:.2}x$'.format(\n", + " theta0=float(theta[0][0]),\n", + " theta1=(float(theta[1][0]) if theta[1][0] >= 0 else float(-theta[1][0])),\n", + " op='+' if theta[1][0] >= 0 else '-')))" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wczytanie danych (mieszkania) przy pomocy biblioteki pandas\n", + "\n", + "alldata = pandas.read_csv('data_flats_with_outliers.tsv', sep='\\t',\n", + " names=['price', 'isNew', 'rooms', 'floor', 'location', 'sqrMetres'])\n", + "data = np.matrix(alldata[['price', 'sqrMetres']])\n", + "\n", + "m, n_plus_1 = data.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data[:, 0:n]\n", + "\n", + "Xo = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n + 1)\n", + "yo = np.matrix(data[:, -1]).reshape(m, 1)\n", + "\n", + "Xo /= np.amax(Xo, axis=0)\n", + "yo /= np.amax(yo, axis=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data(Xo, yo, xlabel=u'metraż', ylabel=u'cena')\n", + "theta_start = np.matrix([0.0, 0.0]).reshape(2, 1)\n", + "theta, logs = gradient_descent(cost, gradient, theta_start, Xo, yo, alpha=0.01)\n", + "plot_regression(fig, h_linear, theta, Xo)" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Odrzućmy obserwacje odstające\n", + "alldata_no_outliers = [\n", + " (index, item) for index, item in alldata.iterrows() \n", + " if item.price > 100 and item.sqrMetres > 10]\n", + "\n", + "alldata_no_outliers = alldata.loc[(alldata['price'] > 100) & (alldata['sqrMetres'] > 100)]" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "data = np.matrix(alldata_no_outliers[['price', 'sqrMetres']])\n", + "\n", + "m, n_plus_1 = data.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data[:, 0:n]\n", + "\n", + "Xo = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n + 1)\n", + "yo = np.matrix(data[:, -1]).reshape(m, 1)\n", + "\n", + "Xo /= np.amax(Xo, axis=0)\n", + "yo /= np.amax(yo, axis=0)" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data(Xo, yo, xlabel=u'metraż', ylabel=u'cena')\n", + "theta_start = np.matrix([0.0, 0.0]).reshape(2, 1)\n", + "theta, logs = gradient_descent(cost, gradient, theta_start, Xo, yo, alpha=0.01)\n", + "plot_regression(fig, h_linear, theta, Xo)" + ] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.14" + }, + "livereveal": { + "start_slideshow_at": "selected", + "theme": "amu" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/w2/zumz182b.pdf b/w2/zumz182b.pdf new file mode 100644 index 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0.7860399993656908 0.2917387997774099 +0 -0.31357941345778184 0.8173465016744779 +0 -0.24706729772892544 -0.5017567368968896 +0 -0.5077834677535535 0.734692375238988 +1 0.9180554343925105 0.7402607565839483 +0 0.7347556198277827 -0.8922440369193774 +0 0.05178553367177474 0.024867950728887367 +0 0.6123243631772981 -0.9310030202911994 diff --git a/w3/create_bayes_nasty.py b/w3/create_bayes_nasty.py new file mode 100644 index 0000000..99a421f --- /dev/null +++ b/w3/create_bayes_nasty.py @@ -0,0 +1,26 @@ +#!/usr/bin/python3 +# -*- coding:utf-8 -*- + + +import csv +import math +import random +import sys + + +def create_bayes_nasty_data(filename): + with open(filename, 'w') as f: + writer = csv.writer( + f, delimiter=('\t' if filename.endswith('.tsv') else ',')) + for i in range(100): + x = random.uniform(-1.0, 1.0) + y = random.uniform(-1.0, 1.0) + p = abs(x-y) / abs(x+y) + # for i in range(2): + # p = -2 * p**3 + 3 * p**2 + v = 1 if random.random() > p else 0 + writer.writerow([v, x, y]) + + +if __name__ == '__main__': + create_bayes_nasty_data(sys.argv[1]) diff --git a/w3/iris.csv b/w3/iris.csv new file mode 100644 index 0000000..2ee7967 --- /dev/null +++ b/w3/iris.csv @@ -0,0 +1,151 @@ +łod.dł.,łod.sz.,pł.dł.,pł.sz.,Gatunek +5.2,3.4,1.4,0.2,Iris-setosa +5.1,3.7,1.5,0.4,Iris-setosa +6.7,3.1,5.6,2.4,Iris-virginica +6.5,3.2,5.1,2.0,Iris-virginica +4.9,2.5,4.5,1.7,Iris-virginica +6.0,2.7,5.1,1.6,Iris-versicolor +5.7,2.6,3.5,1.0,Iris-versicolor +5.0,2.0,3.5,1.0,Iris-versicolor +5.2,3.5,1.5,0.2,Iris-setosa +4.8,3.0,1.4,0.1,Iris-setosa +6.7,3.3,5.7,2.5,Iris-virginica +6.1,3.0,4.9,1.8,Iris-virginica +4.8,3.4,1.9,0.2,Iris-setosa +5.8,2.8,5.1,2.4,Iris-virginica +4.4,2.9,1.4,0.2,Iris-setosa +7.2,3.0,5.8,1.6,Iris-virginica +4.4,3.2,1.3,0.2,Iris-setosa +5.0,3.5,1.3,0.3,Iris-setosa +5.4,3.9,1.3,0.4,Iris-setosa +7.7,2.8,6.7,2.0,Iris-virginica +5.0,3.6,1.4,0.2,Iris-setosa +6.2,2.8,4.8,1.8,Iris-virginica +6.0,2.2,5.0,1.5,Iris-virginica +7.4,2.8,6.1,1.9,Iris-virginica 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Naiwny klasyfikator bayesowski, drzewa decyzyjne\n", + "### Część 1" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 3.1. Naiwny klasyfikator bayesowski" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Naiwny klasyfikator bayesowski jest algorytmem dla problemu klasyfikacji wieloklasowej.\n", + "* Naszym celem jest znalezienie funkcji uczącej $f \\colon x \\mapsto y$, gdzie $y$ oznacza jedną ze zdefiniowanych wcześniej klas.\n", + "* Klasyfikacja probabilistyczna polega na wskazaniu klasy o najwyższym prawdopodobieństwie:\n", + "$$ \\hat{y} = \\mathop{\\arg \\max}_y P( y \\,|\\, x ) $$\n", + "* Klasyfikatory probabilistyczne → klasyfikatory bayesowskie → naiwny klasyfikator bayesowski" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Twierdzenie Bayesa\n", + "\n", + "$$ P( y_k \\,|\\, x ) = \\frac{ P( x \\,|\\, y_k ) \\cdot P( y_k ) }{ \\sum_{i} P( x \\,|\\, y_i ) \\, P( y_i ) } $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Twierdzenie Bayesa\n", + "\n", + "$$ \\underbrace{P( y_k \\,|\\, x )}_\\textrm{ prawd. a posteriori } = \\frac{ \\overbrace{ P( x \\,|\\, y_k )}^\\textrm{ model klasy } \\cdot \\overbrace{P( y_k )}^\\textrm{ prawd. a priori } }{ \\underbrace{\\sum_{i} P( x \\,|\\, y_i ) \\, P( y_i )}_\\textrm{wyrażenie normalizacyjne} } $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Rola wyrażenia normalizacyjnego w twierdzeniu Bayesa\n", + "\n", + "_Przykład_: obserwacja nietypowa ma małe prawdopodobieństwo względem dowolnej klasy, wyrażenie normalizacyjne sprawia, że to prawdopodobieństwo staje się porównywalne z prawdopodobieństwami typowych obserwacji, ale nie wpływa na klasyfikację!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Klasyfikatory dyskryminatywne a generatywne\n", + "\n", + "* Klasyfikatory generatywne tworzą model rozkładu prawdopodobieństwa dla każdej z klas.\n", + "* Klasyfikatory dyskryminatywne wyznaczają granicę klas (_decision boundary_) bezpośrednio.\n", + "* Naiwny klasyfikator baywsowski jest klasyfikatorem generatywnym (ponieważ wyznacza $P( x \\,|\\, y )$).\n", + "* Wszystkie klasyfikatory generatywne są probabilistyczne, ale nie na odwrót.\n", + "* Regresja logistyczna jest przykładem klasyfikatora dyskryminatywnego." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Założenie niezależności dla naiwnego klasyfikatora bayesowskiego\n", + "\n", + "* Naiwny klasyfikator bayesowski jest _naiwny_, ponieważ zakłada, że poszczególne cechy są niezależne od siebie:\n", + "$$ P( x_1, \\ldots, x_n \\,|\\, y ) \\,=\\, \\prod_{i=1}^n P( x_i \\,|\\, x_1, \\ldots, x_{i-1}, y ) \\,=\\, \\prod_{i=1}^n P( x_i \\,|\\, y ) $$\n", + "* To założenie jest bardzo przydatne ze względów obliczeniowych, ponieważ bardzo często mamy do czynienia z ogromną liczbą cech (bitmapy, słowniki itp.)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Naiwny klasyfikator bayesowski – przykład" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przydtne importy\n", + "\n", + "import ipywidgets as widgets\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas\n", + "\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Wczytanie danych (gatunki kosaćców)\n", + "\n", + "data_iris_setosa = (\n", + " pandas.read_csv('iris.csv', usecols=['pł.dł.', 'pł.sz.', 'Gatunek'])\n", + " .apply(lambda x: [x[0], x[1], 1 if x[2] == 'Iris-setosa' else 0], axis=1))\n", + "data_iris_setosa.columns = ['dł. płatka', 'szer. płatka', 'Iris setosa?']\n", + "\n", + "m, n_plus_1 = data_iris_setosa.values.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data_iris_setosa.values[:, 0:n].reshape(m, n)\n", + "\n", + "X = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n", + "Y = np.matrix(data_iris_setosa.values[:, 2]).reshape(m, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "count: {0: 100, 1: 50}\n", + "prior prob.: {0: 0.6666666666666666, 1: 0.3333333333333333}\n" + ] + } + ], + "source": [ + "classes = [0, 1]\n", + "count = [sum(1 if y == c else 0 for y in Y.T.tolist()[0]) for c in classes]\n", + "prior_prob = [float(count[c]) / float(Y.shape[0]) for c in classes]\n", + "\n", + "print 'count: ', {c: count[c] for c in classes}\n", + "print 'prior prob.:', {c: prior_prob[c] for c in classes}" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wykres danych (wersja macierzowa)\n", + "def plot_data_for_classification(X, Y, xlabel, ylabel): \n", + " fig = plt.figure(figsize=(16*.6, 9*.6))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + " X = X.tolist()\n", + " Y = Y.tolist()\n", + " X1n = [x[1] for x, y in zip(X, Y) if y[0] == 0]\n", + " X1p = [x[1] for x, y in zip(X, Y) if y[0] == 1]\n", + " X2n = [x[2] for x, y in zip(X, Y) if y[0] == 0]\n", + " X2p = [x[2] for x, y in zip(X, Y) if y[0] == 1]\n", + " ax.scatter(X1n, X2n, c='r', marker='x', s=50, label='Dane')\n", + " ax.scatter(X1p, X2p, c='g', marker='o', s=50, label='Dane')\n", + " \n", + " ax.set_xlabel(xlabel)\n", + " ax.set_ylabel(ylabel)\n", + " ax.margins(.05, .05)\n", + " return fig" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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ky8xeYmbLqkuWQQFAy/EA/fv27ZOOPDL6Od32uDjK5ebjLJeliy6Kfk63PUQcQKuKq8iX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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[matrix([[ 1. , 4.906, 1.676]]), matrix([[ 1. , 1.464, 0.244]])]\n", + "[matrix([[ 0. , 0.8214402 , 0.42263933]]), matrix([[ 0. , 0.17176728, 0.10613199]])]\n" + ] + } + ], + "source": [ + "XY = np.column_stack((X, Y))\n", + "XY_split = [XY[np.where(XY[:,3] == c)[0]] for c in classes]\n", + "X_split = [XY_split[c][:,0:3] for c in classes]\n", + "Y_split = [XY_split[c][:,3] for c in classes]\n", + "\n", + "X_mean = [np.mean(X_split[c], axis=0) for c in classes]\n", + "X_std = [np.std(X_split[c], axis=0) for c in classes]\n", + "print X_mean \n", + "print X_std" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Rysowanie średnich\n", + "def draw_means(fig, means, xmin=0.0, xmax=7.0, ymin=0.0, ymax=7.0):\n", + " class_color = {0: 'r', 1: 'g'}\n", + " classes = range(len(means))\n", + " ax = fig.axes[0]\n", + " mean_x1 = [means[c].item(0, 1) for c in classes]\n", + " mean_x2 = [means[c].item(0, 2) for c in classes]\n", + " for c in classes:\n", + " ax.plot([mean_x1[c], mean_x1[c]], [xmin, xmax],\n", + " color=class_color.get(c, 'c'), linestyle='dashed')\n", + " ax.plot([ymin, ymax], [mean_x2[c], mean_x2[c]],\n", + " color=class_color.get(c, 'c'), linestyle='dashed') " + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "from scipy.stats import norm\n", + "\n", + "# Prawdopodobieństwo klasy dla pojedynczej cechy\n", + "def prob(x, c, feature, mean, std):\n", + " return norm(mean[c].item(0, feature), std[c].item(0, feature)).pdf(x)\n", + "\n", + "# Prawdopodobieństwo klasy\n", + "def class_prob(x, c, mean, std):\n", + " return prob(x[1], c, 1, mean, std) * prob(x[2], c, 2, mean, std)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wykres prawdopodobieństw klas\n", + "def plot_prob(fig, X_mean, X_std, classes, xmin=0.0, xmax=7.0, ymin=0.0, ymax=7.0):\n", + " class_color = {0: 'r', 1: 'g'}\n", + " ax = fig.axes[0]\n", + " x1, x2 = np.meshgrid(np.arange(xmin, xmax, 0.02),\n", + " np.arange(xmin, xmax, 0.02))\n", + " for c in classes:\n", + " fun1 = lambda x: prob(x, c, 1, X_mean, X_std)\n", + " fun2 = lambda x: prob(x, c, 2, X_mean, X_std)\n", + " p = fun1(x1) * fun2(x2)\n", + " plt.contour(x1, x2, p, levels=np.arange(0.0, 1.0, 0.1),\n", + " colors=class_color.get(c, 'c'), lw=3)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/pawel/.local/lib/python2.7/site-packages/matplotlib/contour.py:967: UserWarning: The following kwargs were not used by contour: 'lw'\n", + " s)\n" + ] + }, + { + "data": { + "image/png": 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6YqLry75dO5HRo0UeeUTkww+1/fHwJRQrgZVI4OKSx45p8Oq+zuHwfNyokedj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\n3fDpjk/RsVFHJCUkocRZ4tGLM7TLUMwePRtJCUm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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n", + "draw_means(fig, X_mean)\n", + "plot_prob(fig, X_mean, X_std, classes)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Prawdopodobieństwo a posteriori\n", + "def posterior_prob(x, c):\n", + " normalizer = sum(class_prob(x, c, X_mean, X_std)\n", + " * prior_prob[c]\n", + " for c in classes)\n", + " return (class_prob(x, c, X_mean, X_std) \n", + " * prior_prob[c]\n", + " / normalizer)\n", + "\n", + "# Wykres granicy klas dla naiwnego Bayesa\n", + "def plot_decision_boundary_bayes(fig, X_mean, X_std, xmin=0.0, xmax=7.0, ymin=0.0, ymax=7.0):\n", + " ax = fig.axes[0]\n", + " x1, x2 = np.meshgrid(np.arange(xmin, xmax, 0.02),\n", + " np.arange(ymin, ymax, 0.02))\n", + " p = [posterior_prob([1, x1, x2], c) for c in classes]\n", + " p_diff = p[1] - p[0]\n", + " plt.contour(x1, x2, p_diff, levels=[0.0], colors='c', lw=3);" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n", + "plot_decision_boundary_bayes(fig, X_mean, X_std)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Dla porównania: regresja logistyczna na tych samych danych" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def powerme(x1,x2,n):\n", + " X = []\n", + " for m in range(n+1):\n", + " for i in range(m+1):\n", + " X.append(np.multiply(np.power(x1,i),np.power(x2,(m-i))))\n", + " return np.hstack(X)\n", + "\n", + "# Funkcja logistyczna\n", + "def safeSigmoid(x, eps=0):\n", + " y = 1.0/(1.0 + np.exp(-x))\n", + " if eps > 0:\n", + " y[y < eps] = eps\n", + " y[y > 1 - eps] = 1 - eps\n", + " return y\n", + "\n", + "# Funkcja hipotezy dla regresji logistycznej\n", + "def h(theta, X, eps=0.0):\n", + " return safeSigmoid(X*theta, eps)\n", + "\n", + "# Funkcja kosztu dla regresji logistycznej\n", + "def J(h,theta,X,y, lamb=0):\n", + " m = len(y)\n", + " f = h(theta, X, eps=10**-7)\n", + " j = -np.sum(np.multiply(y, np.log(f)) + \n", + " np.multiply(1 - y, np.log(1 - f)), axis=0)/m\n", + " if lamb > 0:\n", + " j += lamb/(2*m) * np.sum(np.power(theta[1:],2))\n", + " return j\n", + "\n", + "# Gradient funkcji kosztu\n", + "def dJ(h,theta,X,y,lamb=0):\n", + " g = 1.0/y.shape[0]*(X.T*(h(theta,X)-y))\n", + " if lamb > 0:\n", + " g[1:] += lamb/float(y.shape[0]) * theta[1:] \n", + " return g\n", + "\n", + "# Funkcja klasyfikująca\n", + "def classifyBi(theta, X):\n", + " prob = h(theta, X)\n", + " return prob" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Przygotowanie danych dla wielomianowej regresji logistycznej\n", + "\n", + "data = np.matrix(data_iris_setosa)\n", + "\n", + "Xpl = powerme(data[:, 1], data[:, 0], n)\n", + "Ypl = np.matrix(data[:, 2]).reshape(m, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Metoda gradientu prostego dla regresji logistycznej\n", + "def GD(h, fJ, fdJ, theta, X, y, alpha=0.01, eps=10**-3, maxSteps=10000):\n", + " errorCurr = fJ(h, theta, X, y)\n", + " errors = [[errorCurr, theta]]\n", + " while True:\n", + " # oblicz nowe theta\n", + " theta = theta - alpha * fdJ(h, theta, X, y)\n", + " # raportuj poziom błędu\n", + " errorCurr, errorPrev = fJ(h, theta, X, y), errorCurr\n", + " # kryteria stopu\n", + " if abs(errorPrev - errorCurr) <= eps:\n", + " break\n", + " if len(errors) > maxSteps:\n", + " break\n", + " errors.append([errorCurr, theta]) \n", + " return theta, errors" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = [[ 4.01960795]\n", + " [ 3.89499137]\n", + " [ 0.18747599]\n", + " [-1.3524039 ]\n", + " [-2.00123783]\n", + " [-0.87625505]]\n" + ] + } + ], + "source": [ + "# Uruchomienie metody gradientu prostego dla regresji logistycznej\n", + "theta_start = np.matrix(np.zeros(Xpl.shape[1])).reshape(Xpl.shape[1], 1)\n", + "theta, errors = GD(h, J, dJ, theta_start, Xpl, Ypl, \n", + " alpha=0.1, eps=10**-7, maxSteps=100000)\n", + "print(r'theta = {}'.format(theta))" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wykres granicy klas\n", + "def plot_decision_boundary(fig, theta, Xpl, xmin=0.0, xmax=7.0):\n", + " ax = fig.axes[0]\n", + " xx, yy = np.meshgrid(np.arange(xmin, xmax, 0.02),\n", + " np.arange(xmin, xmax, 0.02))\n", + " l = len(xx.ravel())\n", + " C = powerme(yy.reshape(l, 1), xx.reshape(l, 1), n)\n", + " z = classifyBi(theta, C).reshape(int(np.sqrt(l)), int(np.sqrt(l)))\n", + "\n", + " plt.contour(xx, yy, z, levels=[0.5], colors='m', lw=3);" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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bq6XKpzqkMP65QKfJNrGiQSgKmpmp37R+mjB/gmZWz9Tr//x6DbpikGp+WqPV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\nx/71nF+ryNr+R6/IivTVS7/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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(Xpl, Ypl, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n", + "plot_decision_boundary(fig, theta, Xpl)" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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Eitq8YKa1BurFpUAiIgqJb7nLt8Tme/neB1rusnqprPvyX/fY3O7AS3WBxrf7+Gh2Ht8d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\nBbm5uGvECHwkJweOOF4KU1X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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(Xpl, Ypl, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n", + "plot_decision_boundary(fig, theta, Xpl)\n", + "plot_decision_boundary_bayes(fig, X_mean, X_std)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Inny przykład" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Wczytanie danych (gatunki kosaćców)\n", + "\n", + "data_iris_versicolor = (\n", + " pandas.read_csv('iris.csv', usecols=['pł.dł.', 'pł.sz.', 'Gatunek'])\n", + " .apply(lambda x: [x[0], x[1], 1 if x[2] == 'Iris-versicolor' else 0], axis=1))\n", + "data_iris_versicolor.columns = ['dł. płatka', 'szer. płatka', 'Iris versicolor?']\n", + "\n", + "m, n_plus_1 = data_iris_versicolor.values.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data_iris_versicolor.values[:, 0:n].reshape(m, n)\n", + "\n", + "X = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n", + "Y = np.matrix(data_iris_versicolor.values[:, 2]).reshape(m, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "count: {0: 100, 1: 50}\n", + "prior prob.: {0: 0.6666666666666666, 1: 0.3333333333333333}\n" + ] + } + ], + "source": [ + "classes = [0, 1]\n", + "count = [sum(1 if y == c else 0 for y in Y.T.tolist()[0]) for c in classes]\n", + "prior_prob = [float(count[c]) / float(Y.shape[0]) for c in classes]\n", + "\n", + "print 'count: ', {c: count[c] for c in classes}\n", + "print 'prior prob.:', {c: prior_prob[c] for c in classes}" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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RygtW1jy+6sJVQcYI1UqJFkUAQssz+bpT0h9b5AxJL5eXsQCQo2MOP0ZrF64d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\n4O7bJf3czOaXd10giQeY0vF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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[matrix([[ 1. , 3.508, 1.135]]), matrix([[ 1. , 4.26 , 1.326]])]\n", + "[matrix([[ 0. , 2.08373127, 0.91459007]]), matrix([[ 0. , 0.46518813, 0.19576517]])]\n" + ] + } + ], + "source": [ + "XY = np.column_stack((X, Y))\n", + "XY_split = [XY[np.where(XY[:,3] == c)[0]] for c in classes]\n", + "X_split = [XY_split[c][:,0:3] for c in classes]\n", + "Y_split = [XY_split[c][:,3] for c in classes]\n", + "\n", + "X_mean = [np.mean(X_split[c], axis=0) for c in classes]\n", + "X_std = [np.std(X_split[c], axis=0) for c in classes]\n", + "print X_mean\n", + "print X_std" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/pawel/.local/lib/python2.7/site-packages/matplotlib/contour.py:1180: UserWarning: No contour levels were found within the data range.\n", + " warnings.warn(\"No contour levels were found\"\n" + ] + }, + { + "data": { + "image/png": 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FEitjzJTKDkREpEQLFjibD1uwdQELtvp2G0Vqi4r2WL1VqVGIiIiI+IAyEytjjJ8x5oUT\n91trl3svJBEREZGaqczEylqbB1xwmmIRERERqdE8mW7hV2PMl8CnQFr+TmvtbK9FJSKSLyqqqiPw\nuqhQ32+jSG3hSWIVDCQDFxXaZwElViLifbNmVXUEXjdruO+3UaS28GTm9ZtPRyAiIiIiNV253wo0\nxrQ2xiwwxqw59v5cY8xj3g9NRASYMMHZfNiE+ROYMN+32yhSW3gyFPg28CDHpliw1q4yxnwEPO3N\nwEREAFi6tKoj8Lqlu3y/jSK1hSfzWIVaa38+YV+uN4IRERERqck8SaySjDFn4RSsY4wZBuzxalQi\nIiIiNZAnQ4F/AaYAbY0xu4GtwEivRiUiIiJSA3nyrcAtwEBjTBjgstamej8sEZFjmjWr6gi8rlkd\n32+jSG1hrLVln2BMHvBPYII9drIxZoW1tktlB9OtWzcbHx9f2bcVEREROSXGmOXW2m7lnedJjdXa\nY+f9xxhTP//+pxKciIiIiC/yJLHKtdY+BLwD/M8Y05VjhewiIl43bpyz+bBx88Yxbp5vt1GktvCk\neN0AWGunG2PWAh8BsV6NSkQkX0JCVUfgdQl7fb+NIrWFJ4nVn/N/sNauMcZcCFzpvZBEREREaiZP\nhgLPNMZEABxbyuZdYE15Fxljgo0xPxtjVhpj1hpjnjzFWEVERESqNU8Sq79aa1ONMRcAA4H/A97w\n4Los4CJrbScgDhhkjOlR8VBFREREqjdPhgLzjr1eCkyx1n5tjCl3ncBjUzMcPfY24NimoncROTmt\nW1d1BF7XOsr32yhSW3gyj9VXwG7gYqALkAH8fKwnqrxr/YDlQCvgNWvt+BLOGQ2MBoiNje26ffv2\nk22DiIiIiFdV5jxWw4FvgUustYeB+sCDngRhrc2z1sYBzYDzjTEdSjhnirW2m7W2W3R0tCe3FRER\nEamWPFnSJh2YXej9Hk5yEWZr7WFjzPfAIDwofBcRKTB6tPM6ZUrVxuFFo+c4bZxyue+2UaS28KTG\nqkKMMdFAzrGkKgRnKPEf3nqeiPiojRurOgKv25js+20UqS28llgBMcB7x+qsXMAMa+1XXnyeiIiI\nSJXyWmJlrV0FdPbW/UVERESqG0+K10VERETEA94cChQROXVxcVUdgdfFNfb9NorUFuXOY3U6devW\nzcbHx1d1GCIiIiJFVOY8ViIiIiLiASVWIlK9jRzpbD5s5OyRjJzt220UqS1UYyUi1duuXVUdgdft\nSvH9NorUFuqxEhEREakkSqxEREREKokSKxEREZFKohorEaneevas6gi8rmcz32+jSG2heaxERERE\nyqF5rERERCqLtfDZZ86rJ/sr696zZzubN54rXqHESkSqt6FDnc2HDZ0xlKEzfLuNNd7nn8M118C9\n9x5PZqx13l9zjXPcG/fO//33xnPFK1RjJSLVW3JyVUfgdcnpvt/GGu+qq2DsWJg82Xn/8stOcjN5\nsrP/qqu8c+977nH2eeO54hVKrERERMpjjJPUgJPU5Cc6Y8c6+43x3r3zz6ns54pXaChQREROL2/W\nK50KtxvGj3deS9pv7fFEJ19lJTeFk6sT713WMal2lFiJiMjp5c16pVMxYQJMnAhdux5Prtxu5/3E\nic7xe+8tek3hNpyK/PaXdO+yjkm1o8RKRKq3AQOczYcNaDmAAS19u41FFK4pyk8QqkPd0HPPQVwc\nJCQcT666dnXex8VBRsbxGN3u4m2oqBPbX/je48Y5mzeeK95hra02W9euXa2IiNQCbre1Y8fm98c4\n29ixzv6qlJdnbVxc0bji4qydObN4jIXbMHt2xZ85e3bZ9/bWc+WkAPHWg1ymypOpwpsSKxGRWsDt\ndhKCvLyiCUxe3vH9s2cXT7LcbmtnzXK2ko6Vd21J+0tSUlx5edY+9JDzeuK5Je335NmexDxzprUP\nPlix59ZU5X1eVZR8K7ESEd8waJCz+bBBHwyygz7w7TYWkd9DU1LPEDgJQ0V7cMq7trweHm/0WJXX\nI+Wta2uqatpmJVYi4hv69nU2H9b33b6277t9qzqM06dw8hIXV/x9bu7xP6L5f1zz399zj7OVdGzs\nWOdepV1b3lBjWXF16lT2c8u6b0nnno5ra6pq2mYlViLiG5RY+Z7yeqzyh3tKq8Eqrz6rovVb+b1d\n+UmVtUWTqwcfrHhd2KnUlFXXejRvqoZt9jSx0iLMIlK99evnvC5cWJVReFW/qf0AWDhqYZXGcdpY\n60ypcOWV4Od3fH9eHnzxhfOtQGOc81yFvrzudh+fu6msY54cL4nb7Uyp8Nxzxa/N32/Myd/3VGKq\njGtrqmrWZi3CLCIi1ZMxTvJ0331F9993X9GkqqLzOpV3vKy4evQo/sc7f3/+fUqLqaxJT93uis9F\nVdH2VKXyPo/yYq+Jbc7nSbfW6do0FCgixfzzn87mw/65+J/2n4t9u41FlFdDU1adlDdrrMormr70\n0tLvO2tWxa/1xRqrUylAr6ZtRjVWIiJSLZX3R7eqvhVY1h/0ExOjE8+fNavi1/ritwJPJTmqpm1W\nYiUiItXTqczr5O15rEormvbkvqdybUU/q+raY2VtxQvQq2mbPU2sVLwuItWbitflZNhjhfH5tVqF\n93/2mfPz1VcXP5ZfTP/FFyUX1eevX1jatWUV3EPpMZW0vyYo63Mu7/OoaW09RsXrIiJS+5S1wPPQ\noc5W2uLPEyY4r127Fr1n167lX/v556UXXH/2WfVcdPpUeLKQdmmfRzXq0PEKT7q1TtemoUARKUbz\nWMnJKKu2p7zC99zcik8QeioF99V5OK80p/IFhBraZlRjJSI+QYmVnKyKTi5a3sSlhQvUS7vWk+L2\nk6k3qs48+SyrWQH6qVBiJSK+QYlV9VSdC9Dzzy38B7/wNaUdK/z8wscLx1PeteUVt5cWU1WojCLx\n0tp0KotWV1NVnlgBzYHvgXXAWmBsedcosRKRYl57zdl82Gs/v2Zf+7mGtbG6TplQ0nM87bE61Wsr\nGlNVOdVeJfVYnfbEKgbocuznCGAj0K6sa5RYiYjUEKdSY+PNST5PpcbKW3VSpzKnkzedSlyqsTr9\niVWxB8EXwMVlnaPESkSKSUtzNh+Wlp1m07JrYBu92ftT0R6e8npKvNXLVlMn+fTW51zeQto1ULVK\nrIAWwA6gTgnHRgPxQHxsbKw3PxMRqYlUY1W9VaReaeZMJ4nJzS16LDe3aP1NSfeuqtqu8q4tr3en\nOk8QWpHaL0/jqm51Zaeg2iRWQDiwHLimvHPVYyUixSixqr48qbEp7Rt2YG2DBkWP5b9/6KHS713e\nmnw1sHanTN7u7fJmr5J6rLySVAUA3wL3eXK+EisRKUaJVfVUXo1NeXNCRUUdT6Zyc48nVQ0aWJuT\n451ap5rIm/VZNfXeVaTKEyvAAO8Dkzy9RomViBSjxKp68vRbgRXtsSrr3r44J1RZvNXz483esOpc\nV1ZBniZWXlsr0BhzAfA/YDVwbLEkHrHWzi3tGq0VKCLFaK3A6snasteK82TdvSuvBH//48dyc+HL\nL49fW9Y6dOAza9B5xNrKb295/w1PZQ1Db967ilT5WoHW2kXWWmOtPddaG3dsKzWpEhEp0ahRzubD\nRsWNYlTcqKoOozi3G8aPJzXjCO+seIfx/x3POyveITXjCIwfD0uXOn8oC7MWfvrJ+fmqq+C++4oe\nv+8+Z7+1Ja/Jl58wnLjYMRzfDxVbg+5YewoWRj5xf16es65fSW0qab8n51TGtW53xdfcK+vepSU4\npX3+J6O8/4Y1LKk6KZ50a52uTUOBIiLVyEMP2f/FYiMeddmwZ8Isf8OGPRNmIx512f/FFhray/8W\nX+E6qoceKr3GZsiQ40NanTo513XqdHzfzJmlx3QqtTuFhydLivmqqyo+fHUqQ1/lXXvppRVr76nG\nJUVQ1TVWFdmUWIlIMQcOOJsPO5B2wB5Iq35tTEk/bCMedVn+RrEt4lGXTe3SoWiiUrhYfebMsv+g\n52/33OPszy9IB2sffLD0oE4lUTgxxhPf5+Z6b8LMil57YlJ1Mu091bikCE8TK6/VWFWEaqxEpJhq\nUGOVmZvJoYxDHM48zOHMw6RkpRT5OTU7laPZRzmafZS0nDQycjLIzM0s2LLzssnOyybHnUOuO5dc\ndy557jzc1o3buklOTwYgKjQKYwwu48LP+OHv8sff5U+AXwCBfoEE+gUS7B9MkF8QIQEhhPiHEBYQ\nRnhgeMFWJ6gOdYPrUje4bpGf64XUIzQg9KTa/c6Kdxg3bxxpOWnFjoUFhDH5kpe59c+vQ0LC8QNx\ncbB8uTPUU1qNzezZsGwZZGXBK68cP3bPPRAUBM8/X7SeqDB7irU7brcz5FhSzC6Xc59774XJk48f\nHzsWXn65/OErb1z70kvl15t5My4p4GmNlRIrEanevJRYZeZmsjtlN4mpiew9upe9R/ey5+ge9hzd\nw76j+9iftp8D6QdISk8iPSe9zHsZDOGB4YQFhhEaEEpoQCgh/iFOEuQfVJAUBfoFFkmYDE4S9fWm\nrwG49OxLsVjc1k2ezSPPnUeOO4ecvBxy3Dlk5WaRlZdFZm4mGTkZpOekk56TztH0w6TZLNzWXWac\nwf7BRIVEER0WTcOwhjQKa0RMeAwxETE0Dm9M4/DGNIloQtOIpoQFhjH+v+OZuGRiqfd7uPfDPHfR\nM8WL0wslRalZqUxfO51NyZs4O+psRrQfQURQhHPQeqEg2xNud5kxn1JcVXVtVd67lvA0sfIv7wQR\nkZooOy+bLYe2sOXQFrYe2sr2I9vZdngbWw9vZfvh7RxIP1DsGn+XP43CGtE4vDGNwhvRvmF7GoQ0\nICo0inrB9agXUo/IoEjqBNUp8nNYYBgu48JaS1ZeFmnZaQVJT2m9VoV7rJbsWgLAJa0uwWVcRXqs\nTuytCvYPJsQ/hNCAUMIDwwme8w1m6FDs2HvImPgsR7JSOJJ5mEPP/42UL2Zw5NH7OXxuaw5mHCQ5\nPZnkjGQOpB9gf9p+NiZvJDE1key87GKfRb3geoQHhuNn/MizecWOhwWE0aremSUXoB/r/Vm0YxFD\nPhyC27pJy0kjLCCM+769j7k3zuWC5r1LLsj2di9Kfo9VKTEX9O5UJK6qurY83ry3FKPESkRqtCOZ\nR1i9fzXrDqxjfdJ6NiZvZEPyBrYc2lKkByfIL4jYyFha1mtJl8ZdaFanWcGWn0g1CG2Ayzj/V380\n+yh7Uvew9+jegt6rzQc3czDjIAczDnI48zBHso4UDBHmDwnmunMr3JZrP732pK/xM36EPx5IndRX\nqPvUh9Q9sx11N++i7tat1Ls2jqiWEUTl5XBmvTPp0awHjcMbExMeQ52gOhhjsNZyMOMg+9L2sSd1\nD4mpiexO3c2OIzv4/eDv7D6y05mV8ATp2Wl8/O/7SIg5StuWTWn3wnt0uH4c0T8nQNeupC5ZyJAP\nh5CanVpwTf6Q4pAPh5C4byThk984PiRVeKjKW3/wCw8D5g//5b/v2hXi4+H++504TjauwsNtp/Pa\n8njz3lIiDQWKSPV2bCjQfv89u1J28UviL6zYs4KV+1ayet9qth/ZXnBqiH8Ireq3ok2DNrSNasvZ\nUWdzVr2zOLPemTQKb1SQNOW6cwsSh22Ht7H9yHZ2HNnB7lRnaDAxNZGUrJQSwwkPDC/ovaoTWIeI\noIiCuic/lx8u48Icy0Tyh/WsteTZ4z1U+fssTrHr4p2LAejVvJdTY4ULYwzGGPyMX0EPVv4+17GZ\ncvLvkevOJXvFL2Ru+52jQZASBIcb1uFgKKW2IzQglKYRTYmJiKFZnWY0r9Oc2MhYWtRtwVn1zqJl\nvZYEPvJXFn0ykcE3GdwhIaTnphPkF4TNzqbvNktyCGyKdpEacDyBjcnwp+PuXEyLFiwM2kNWXlax\nZ4eZICZ/nsWtfQrV+RROAGbPPj6tQmUaPx4mTixaU1U42brqKqduaWwF4vrsM7jmmtN/bXm8ee9a\nRjVWIlKjpeek88vuX0ie+gabDm7ipdhd7E/bDzi9NG0btKVjo46c2/Bczm10Lu0btic2MrYgeQI4\nkHaAdQfWsfbAWtYnrWdD8gY2H9zM9sPbiwxv+Rk/mkQ0oVmdZsSEx1A/pD4hASH4u/zJdeeSlZtF\nWk4aKVkpJKUnkZSexMGMgxzKPFRuXVM+f+MM6/m7/IskYC7jKkg+gvyCAMizeU4y5s5zkiZ3tuc9\nYRZCc6BRw5Y0DGtIVGgUdYN0Y4G6AAAgAElEQVTqOnVfx9qU584jIzeDI5lHSDyayK4ju9iZsrPI\nZ2IwNI9szlkHoWXXAaTnZGCxdIvpxu1dbiPiiWecxz33HIlpe1l7YC2r961m1b6VrE74llV+ySUO\nIeZ7OPpqHrllKtPXzThef9VuOBHfLPDe5JFuN0yYAM89V7zeaMIEePZZZ4LSihSKl3fvE/cXdqoF\n+WXx5r1rGSVWIlKjZOZmsnjHYhZsXcD3274nPjG+IJk4p8E5nN/0fLo16cZ5Tc7j3EbnEhIQUnCt\n27rZlLyJ5XuWs2LPChL2JrBq36oidVThgeG0jmpN66jWnFHnDMICw/AzfmTkZXAg7QBbD29l2+Ft\n7Diyg8zczGLx1Q+pT2RQJKEBofi7/J2aKmxBYXl+LVV+bZWnCVdFGUxBobwxhgNH94MF6wJzrC75\njHotcRkXRzKPcDDjIG6KxhTgCiA6LJp9R/cBTkIX4ArAYBjeYTgAmw9uZn3Seg5nHi64rm5wXTo0\n7EBcozi6xHSha5OutItuh7/reHXJm/Fvcu+395b4WQI0DGvIoYxDBYllWIBTpzb3xrlcEHtBZX9c\n3qeeIZ+nxEpEqr1th7cxZ8Mc5m6ey8JtC8nMzcTf5c/5Tc+nT2wfesf25gJzBnWD60Lz5gXXpWSl\nsHTnUhbtWMTSXUv5effPBbU8QX5BBT1Z7aPbUz+kPjk2h90pu1m9fzVr9q/h94O/F+lNqRtUlyZ1\nmhAZFEmAK4Bcm0t6TjqHMw6zL20fGbkZxWL3M36EBYQRHBBc8A2//CG/XHcuOe6cgoL1ykyygvyc\nbxnm9365jIt9qXuxHnQ6BPkF0TCsIfVC6hUkMkt3LS01vhZ1W9ChYQc6NuzIGZFnEOQfRGpWKusO\nrGP1/tWs3LeSo9lHAWcYtktMF3o170Xv5r3p1KgT5755bpEaq3yBfoHkufNK7NEKDQhl7/17j39z\nsKYoq5ZJUxv4BCVWIlItbT64mRlrZzBz3Ux+3fsrAGfXP5shZw/h4jMvps8ZfYr+Ue3XD7e1LJz6\nBP/9/b8s2LqA5XuW47ZuXMZFp0ad6NGsB+c1OY9W9VuRnJFMfGI8P+/+mfjEeA5lHgKcHp6z6p1F\n88jmhAWGkefO41DGIXam7GR36u4iMUYERhAZHEmQXxBu6yYzN5MjWUdKnXYhP9nxc/lhMM50Ce48\nsvOcIbwTe4oqymAIcAUUSaqystJJd2eVWGCeL9g/mMigSEICQvAzfmTnZZOSlcKRrCOlXuNn/Ggd\n1RqATQc3FfQehgWE0bVJV85vcj7nNT2PmPAYdqbs5Jfdv/DT7p9YnricHHcOAGfWPZOdKTuL9UqN\n6TaG1355rcT5sQAahTXils63MKL9CM5tdC6mpiQkmi/KpymxEpFqIyUrhU/WfMK7Ce/y0y5nHbme\nzXoy9JyhXNHmCs6OOrvYNYcyDvHlhi/peuMDHMo4SJ8/ufF3+dO9aXcuankRfc7oQ7sG7YjfE8+C\nLc7w4er9qwEnKWgf3Z5zos8hxD+E1OxUth7eypr9awqmFgh0BdKkThMiAiPIs3kczjzMvqP7ivSi\nBPkFER4Yjr/Lnxx3DmnZaSUWY7twEejvzFEFFNRG5dqKf0OwLP7Gv6BWK38Kh9K4jIvIoEj8Xf5k\n5DoTl57MNxf9jB/nRJ9Dq/qtqBtUl+y8bDYf3EzCvoSCzzIi0Cngb9ugLS/94SUy8zL5cdsPfP/L\nDBZlbiQzN9O5T4NzuLXzLWyK/w+vH5xX6jNbRJ7BzpRd5Nk8OjTswKhOo7ip0000DGvo+YdUVTRf\nlM9SYiUiVe63A7/xyrJXmLZqGmk5abSPbs+ouFGMaD+C5pHNi52fkZPBlxu+ZNqqaXz7+7fkunNZ\nMi2QqJAo1s98k/4t+nMo8xCfr/+cLzd8yY/bfyTHnUOIfwi9Y3vTpXEXXMbFtiPb+N/2/xX0RIUH\nhNOqfivCAsM4mn2U7Ue2F9QMGQwNQhsQGhBKdl42yRnJReZ1CnAFEBYQBgYysjPIchdPrAJcTg9S\n/lBgWYlOZfI3Tk1TWQmcH34EBwSX2DvkMq4yhymbRjSlRd0WZOZmsuXQloLevwahDbgw9kJSs1KZ\nv3V+seta1m3JbcG9uPqxD2lx41/4311X8M3v85izcQ6bD27GWDAW3CXUcodlweSz7uTK65/k07Wf\n8v6q9/lp108EuAIY1m4Y43qM4/ym55f30VQN9Vj5NCVWIlJlVu5dyZM/PMln6z8jyC+IGzrewB3d\n7uC8JueVOKyzKXkTr/3yGu+tfI/DmYdpVqcZ13e4nmvbXUu3Gx8k153LOy/eyAerP2DJTmcyzXbR\n7bjs7MtoF92OrYe38vWmr4lPdP79aBDSgM4xnQn2D2ZP6h5W7V9VkCzFRsYSHhBOWk4au471ioAz\nxBURFEF2XjaHMg5hcf5tNBjCAsMwGDJyMoolMX7GjwC/AKy15LhzKlxPFeAKICo0qshs6+X1RuXH\nlx9rRY6XpXmd5uxO2Y0bZ9i1Y8OONKvTDLd1k7A3gT1H95R7j3P3wo11ejPy0enEPD6R3z56hQ9u\n7sbzIfEl1oVF2AASJyQTXmg4eN2BdUxZPoV3E94lJSuF/i3680TfJ+jbom+F2uUVqrHyeUqsROS0\nS0xN5OH5DzNt1TQigyK5p/s93H3+3USHRZd4/sq9K3nqx6eY/dts/F3+DG03lD93/jP9W/bHZVz8\nuudXQi4ezP60/fQdZenQsAM3dLiBS1pdwqIdi3hv5Xus2LMCgO5Nu9MlpgspWSks2rGoYH6rtg3a\n0iCkAUkZSWxM3ojbugnyCyImPAaLZc/RPcWGtI5mHy1SsB4aEIrLuMjIySg2VBgbGUvzyOY0iWhC\n4zBnotHo0GiiQqOoH1K/YM2+2b/NZsL8CaTnFq/TchkXreq3YsNdG4ody3U7hfRHs48WrFF4KONQ\nwbQPj373aInF9ZXprHpn0Ti8MUeyjrBu/zrcuAn2Dy71G3/gLM9zyVl/4OOvnmep/x783HDFBrin\n2VD6TpzBoh2LGDT1IrLdeeQeW13GzxpeHjyZu7vfXeI9U7NSeXvF27yw5AX2HN3DkLOH8NIfXqJN\ngzbeaPbJ0bcCfZ4SKxE5bay1vLPiHR747wNk5WYxrsc4Hr7gYefbfCXYk7qHh+Y/xAerPiAyKJK/\nnPcX7u5+N43DGwMQnxjPX7//K/M2z+Pa34Pp16IfPcc8S2RwJP9c/E/eX/U+6TnpdInpwrXnXEue\nzWP62ums3r+aQL9ALoy9kMigSNYcWMPG5I0AtIlqQ2hAKNsPb+dg5kHAGepyGRd7j+4t6BmqH1If\nay2HMw8X9PQ0r9Ocjo060j66PW0btOXs+mfTqn6rIpOOlqe8dfeGnjOUmcNnevaBFxLw9wCv1XIF\nuAJoF92OXHcuvx34DTdumtdpTpeYLizcupAj2aUXvxsM13W4jvG9HiK0Q2fe6QL/7gxJYU4S/FT/\np+jZrAfTe9ZhTTTsioRF3Ruz9+heBrcazMuXvFxqwpSRk8G/fv4Xz/zvGTJyM3i8z+M8fMHD+Ln8\nSjz/tNB8UT5PiZWInBbpOenc8sUtTF87nf4t+jPl8im0qt+qxHOttby38j3GzhtLVm4W9/a4l/EX\njC9IwJLTk7n/P/fz3sr3aBDagPt63MeY88aQ687lse8e450V7+Dn8mNkx5Hc0vkWFmxdwKSfJnEo\n8xDdmnRjcKvBrDuwji82fEGuO5fuTbvTILQBv+79lcTURMICwmgT1YZDmYfYengrAE3Cm+Dv509i\naiK57lzCAsI4v+n5zjp8fsH0iu3FrZ1vPeWv/7+z4h3GzRtXYq1TWEAYkwdN5tYut5Z5j8SURCYs\nmMD6pPW0bdCW5wY8R6c3O5GUkVTqNeGB4VhrS/0GXmkMhtjIWFKyUjiUeYiwgDAahjUkwBXA5kOb\nyx3ybNegHTtTdpKancqwtfDCf6BhGky9tz/PN/mdHUd2cGl2C15/bRuxx/KzjLF/4V/XxvLM/54l\nIzeDJ/s9yUO9Hyo1ed17dC9j541lxtoZ9D2jLzOHz6RBaIOTamcRSo6kDEqsRMTrUrJSGPzhYJbu\nXMqzA54t849grjuXMV+N4Z1f36HvGX15+/K3i3wb8MftPzL80+EkZyTzQM8HmHDhBOoE1eGbrybz\ntx+eYHnEUcZ0G8OECyewZOcS7pp7F/vS9nFFmyu4tfOtfLruUz5Y9QHhgeGM7DiS7LxsPlrzEZm5\nmfQ9oy+hAaH8sP0H0nPSaRvVlvDAcFbvX01WXhat6rfi6rZXM+TsIVhrufKTK4ssHFwZE1emZqXS\n9KWmJc7rFBYQxo83/0iXmC6lXv/6L6/zl7l/KbZ/XPdxTFo2qdTr5o+cz+WfXF7icGGwX3C5317M\n/6ajtbZg2gh/48/gswczZ+OcUq977qJnuW32NiavnMKLffyxAQH8I+V87pr4A9n33Mmrwav4m/8i\nXAGB/N+107j27SUF9Uh7nxrPXd/czazfZjHk7CFMHzad8MDwUp/1/sr3GT1nNGfUPYPv/vgdTes0\nLfXcMmk4T8qgxEpEvCrPncegDwexcNtCPh76McPaDSv1XLd1c/2s65mxdgaPXPAIf+//9yLDNp+u\n/ZQbZt/AWfXO4pNhnxDXOA5rLY8seIRL/vy8sx7f/5bSOqo1d39zN28tf4suMV14bchrHEg7wB8/\n/yPpOenc3/N+zm10LmPnjeVA2gFuPPdGmkc055WfXyEzN5NrzrmGtOw05m6eS4h/CH/s9EdujruZ\n85uejzGmzOQnIjCCxPsTy/wDX55FOxYx5MMhxZK2s+qfRWRQJAtHLSzxusSURJq+XHqy0Lt574L1\nBgvr36I/X1z3BY1fbFziHFwh/iFl1med3+R8VuxZUWridU3ba5i9fnax/W2j2rI+eT2Xb4APG47h\n8N8e5o65Y5i7aS4js9ry73+sJ8AN2+69mRvar2fprqW89IcXuXf6joIExl51FW/Gv8ld39xFr+a9\n+M/I/xSZbf9Ei3csZvCHg4mNjGXZn5cRFhhW6rmlUgG6lMHTxMqz4gARkRO8+vOrzN8ynzcvfbPM\npApg4uKJzFg7g4kDJ/LMgGeKJFXLdi3jhtk30L1pd5b9eRlxjeMAeOrHp3h+8fPERMTQuXFnzok+\nhz9+/kfeWv4W43uP56dbf2J90nqu+OQKzqx3JqvHrKZxeGOun3U9MeExLL5lMalZqTy3+Dn6nNGH\n9696n4XbFjJ/63we7v0wO+7dwZuXvUn3Zt0Lvqk4fe30Uoe43NbN9DXTT+kzuyD2AhLvT2TyoMk8\n3PthJg+aTOL9iUQGRZZ53YQFE8o83qp+K5bespTo0Gj8jT/RodEsvWUp3/3pO6avnV6wKPSJcvLK\n/sbh8j3LS02qXMbF7PWzGd11NMPOGVbQhvt73s+6v6xj8iWTmNvGxZBzVxMd3pCvrv+Kp/o/xQdB\n67ntpX7YmTNp8eL/8f2fvmdYu2Hc95/7mXlbb6dX6KqrMMYw5rwxfDz0YxbvWMzYeWPLjLV3bG9m\nj5jNugPryv28SmWMkzyNHeskUy6Xkio5aUqsROSkZeZm8vSPT3PJWZdwS+dbyjz3QNoB/v7D37nm\nnGt4sPeDRY65rZvb5txG04imzLl+DpHBzh/nhL0J/G3h37jp3JtoHdUalzG8s+IdPlnzCf8Y+A+e\nH/g88Ynx/PnLP9MisgW3dr6VtfvXMnbeWK5uezXL/ryMN+Lf4MsNXzLpkkk8c9Ez3PbVbdQPqU/C\n7Qk8N/C5EmtxNiVvKrUWKS0njc0HNwOwMWkjvd7pRcwLMfR6pxcbkzYWnJeYksifPvsT3d/uzp8+\n+xOJKYlF7pOSmcKP23/ku63f8eP2H0nJTCn32vVJ68v8jDckbaB9w/Y8O+BZ7ut5H88OeJb2DduX\n26byit6jQqJKPea2brrGdGXK8ikMOHMAyQ8lc3Pczby49EXmbprLPT3G8tGwj1m0cxFPLnwSYwyP\n9XmMx/s8znuHF/JFez8whiD/ID685kPOb3o+d879C0cvvbhIAjO8/XDu63kfb694m9X7VpcZ78Az\nB3J719t5/ZfXSUxNLPPcUuUnV4UpqZKToKFAETlp87fM5+JpF/PV9V9xaetLyzx3yvIp3P7V7ay6\nYxUdG3UscmzZrmX0+L8evHvlu4yKG1Ww/46v7uDD1R+y896d1B10FQBthu0hKiSKxbcsZvHOxfR/\nr3+RZVYycjNoGtGUjXdvZGPyRjq92YlHL3yUpy96mounXczqfatJuCOh4JuHJfGkwHztgbW8/NPL\nxY7f2+NeWtVvVWId1GtDXuPO8+4stU7q7PpOrdmmg5tKvHbZrmW8v+r9UuMedNYgFu9cXGJd2Pqk\n9dw9924y84pPjeCHH3kUX68vX89mPVm5d2WJU0QE+QXx6uBX+WjNR/x24Dd23bcLt3XT4fUONAxr\nyKJbFgFww6wbmLNxDgcePECwv1PT1eZfbTir3ln856b/FNzvx+0/0ndqXz665iOu73h9kWcdzDhI\n4xcac1/P+3h+4POlxgvOpLTtXm/HW5e9xeiuo8s8t0Sa5FNKUSNrrCJaRtiuT3Qtsm94++Hced6d\npOekM+TDIcWuGRU3ilFxo0hKT2LYjOLDEWO6jWFEhxHsPLKTmz67qdjx+3vez+VtLmdD0gZu/+r2\nYscf6/MYA88cSMLeBMbNG1fs+LMDnqVX814s2bmERxY8Uuz4pEGTiGscx/wt83n6x6eLHX/rsrdo\n06ANczbM4cWlLxY7Pu3qaTSPbM70NdN5I/6NYsfzvwUzNWEqUxOmFjs+98a5hAaE8vovrzNj7Yxi\nx/NrOl5Y8gJfbfyqyLGQgBC+ufEbAJ764SkWbF1Q5HhUaBSzhs8CYML8CSzdtbTI8WZ1mvHBNR8A\nMG7eOBL2JhQ53jqqNVMunwLA6DmjC74Wny+ucRyTBjlFuSNnj2RXyq4ix3s268lzA58DYOiMoSSn\nJxc5PqDlAP7a968ADP5wMBk5RWtJLmt9GQ/0egCAflP7cSL97pX+u7fn6B42Jm9k+7jtfLf1uzJ/\n9wa+P5Dvtn5HnzP6FDm+cNRC3kt4j1FfjOL8pucT4n+8fmbVPicJ+2HUDzz1p5YsqHeIH+odoUVk\nC5rVacZPu34qsbfFYOgd25ucvByW7V7G7/f8zivLXuHVZa8SExFT8G3F0n738tx5LN21tMTFgf2M\nH3GN41i+Z3mxY57oGtO1wtfGNYojYV9CqcdduEpcjzAsIIz20e35OfHnCj33ixFfcM2Ma0r8PAJd\ngXx949f85eu/sPHgRro37U6wfzCbD24mOSOZjEczmL9lPnd/czfrk9ZzXpPzCA0IBZwpLX7e/TNv\nXPpGwe+exfLj9h85I/IM/nfz/4r97v2y+xdCA0NpH92+3H/3Fu1YxEO9H6JZnWYn/+/e5m1888x2\nGDuWp66uz4L/ToHdu6FpU2jVSv/uVbN/90qrS/QG1ViJiNfkL6VyIO1AueeGBoRisSWuTxcV6gw1\nZeUWXSYmwC+AHUd2YK2Ffn3hjDPwM35k5GawP31/qTOJWyz70/YXJGn5Q0dB/kElFqSfyM/lR8dG\nHY8vY4OTUPkZZ/+m5OI9Sp5ae2Btha/dcmhLqXVSQKmfh9u62X5ke6nXBvoFlrr+3mtDXiO2bmyx\nXkbXsT8bY84bQ2hAaEHvXoArAICM3AzqBdcrOD8zx+kpC/ALKNiXmJpYbCg2/3cg/z4nti/bnY2/\ny7/EWAvLdeeSZ/OoE1Sn3HOLSUqCbduP91BhoFUrJ6navds5LlKOatVjpaFAkZohMTWRZi8146He\nD5U7NLM8cTnd3u7GxIETi9VYpWal0uSlJlzU8iI+H/F5QRH5tJXT+OPnf+T9q97npk7O//XePud2\npq6cynXtrytzWOyK1lcw49oZdHyjI+k56fww6gf+u+W/jPl6DPf2uJcX/vBCuZN67kndw8PzH2ZD\n8gbaRLXh+YFOEX3MCzHsTdvryUdUTFhA2EnPJZUvJjzGo+VjStK9aXeW7V5W6vGHez/MrZ1v5Y+f\n/5Fth7fRom4L3r/qfVpFtcJayyvLXmHct+MYdNYgWke1ZtZvs0jPSWfDXRv4Lek3Lp52McPbD2fa\n1dP4csOXXPnJlTze53Ge7P8kO4/spPNbnekc05n/3vRfwOlNuvDdC3my35M83vfxgjjGzRvHK8te\nYePdG4vNgzZz3Uyu/fRaPr3203K/KPFW/Fvc8fUdLLllCT2b9zy5D0vzWEkZ1GMlIl7TJKIJIzqM\n4JVlr7AhqfgyLIV1bdKVS8++lL/98DdW7VtV5FhEUASP93mcLzd8yQtLXijYf33H6+ndvDe3f3U7\nv3z9NiQk8PRFT9MwrCGfrf+MYP/gEp/lMi7mbJzDS0tf4pOhn5CRm8F5b59HveB63HX+Xbz808v0\nm9qPtftL7z1atGMRbf7Vhlm/zWLZ7mXM+m0Wbf7VhkU7FtGybsuT+JSKahTeqMLXtqjbotQ2B7gC\nCPQLLPFY/oSo+b1vJR23WLpM6cKqfavYc3QPq/atosuULsxaN4uhM4Yy7ttxXN32asb1GMdn6z8j\nOSOZT4Z+wtebvuaSDy7hzHpnMumSSXy46kOGfzqcbk26Mf6C8Ww7vI2B0waSnZfNvwb/C4C1+9cy\ndMZQzqx3Jvf2uLcgjk/Xfsory17hjm53FEuqElMTueebe+jQsANXtb2qzM8pKT2JJxY+Qfem3enR\nrEeZ55bIGGeeqhOTp9L2i5RAiZWIVMhLf3iJkIAQrvjkCvYd3VfmuW9f/jZ1g+ty8bSL+XXPr0WO\n3d/rfoa3H85D8x/i4fkPk+vOxd/lz+wRs2lRtwXpd93OrluGERUaxfyb5lMnqE6pa9QFuYK4+pyr\neeS7R7jtq9t4+Q8vc1b9s7hu1nUk7EngoV4PsXr/ajq+0ZHrZl7Hkp1LKNxrn5qVypAPh5CanVrQ\nu5SWk0ZqtrN/4sDSl6Qpz/tXlt7LVp7Xh7xeaptz3DklDp+Bk2g+P/D5UnvojDG89vNrJbZ32KfD\nmLtpLneff3fBnGWBfoG8edmbTFwykZu/uJnuTbvzwdUfcOfcOxn52UjOb3o+39zwDbN/m03ntzqz\n7+g+5t44l9ZRrflkzSf0/L+eTlH9DXOJCIrAWsury17lulnX0at5L178Q9Fav22Ht9H/vf6kZKXw\n8dCPyxwKPJp9lKunX82hzEO8ddlbJS72LXI6KLESkQqJiYjhi+u+YFfKLi5898IypwSIiYjhuz9+\nR6BfIL3/3Zu3l79dkNC4jIsPrv6A27vezj8W/4ML/n0BK/eupGFYQxbfspj6IfXYfPB3Lvj3BRzK\nPMSK21fQs5kzxJNfOxTocnpsstxZhPiH8I+B/2B/2n7+9MWfcOHi5rib2XhwIxOXTKRxeGP6t+zP\n15u+pve/e9PhjQ489cNTrNm/hk/WfFLmPFZvJ7xd6h93f5c/N3a8scRjrw15jd+Sfyu1Z8lgyqx1\nit8TT7BfyT1WwX7B3HXeXUQERhT0TIUFhBERGMHcG+cSExHD3Bvnlnj8zm53llqf5TIuGoc35tWf\nX2Xh9oXc2PFGWtZtyajPR7Fizwr+1vdvtI9uT+9/9+aL9V/w935/57E+j3HV9Ku46bObaBPVhuWj\nlxMVEsUVn1zB9bOup110O37+88+0adCGrYe2ctnHl3HPvHu49OxLmTdyXpEJQL/c8CXdpnRj39F9\nfDvyWzo07FBinOAM3Q58fyBLdi5h2tXT6NS4U6nninibaqxEhNSsVKavnc6m5E2cHXU2I9qP8Hht\nvCU7l3DlJ1eSmZvJpEsmcUvnW0rtLdh3dB83zL6B77Z+x4CWA5g0aFKRP5jT10znrm/u4mDGQW6O\nu5nH+jzGGVeNYt/RfXS67iD70/Zz6dmX8kDPB0hMTeS+/9zHvrR9NA5vzB1d7yApPYl3E94lLSeN\nHs160LJuS5btWsaWw1uIDIrk3IbnsidtT8F8VPWC6+EyLg5mHMRiqRNUh5SslBJjB8/qlcb2GOvU\nZyVtoE0Dpz6rcXjjchdhbl6nOT/f9nOFrn2498M82udRpq+ZzuaDm2lVvxUjOowoMkv80eyjBcej\nQ6NpGN6Ql5e+zIq9K0q9b53AOnRq3IkNyRvYn7afxuGN6RPbh6SMJL7f+j3+Ln9u6HgDHRt2ZPra\n6fyS+Asx4TE82e9JusR04eWfXubjNR8TFhDGE32fYGyPsRzMOMg/F/+Tf/3yL/yMH89c9Ax3d7+7\noFdt++HtjJ8/nulrp9OpUSc+vfbTIksfnWjOhjncNuc2UrNT+eDqD7j6HC05I95RI6dbUGIlcvqV\ntszKyayNtytlFyNnj+SH7T/Qv0V/Jg+aXOzbZPnc1s1b8W/x6HePciTrCDd2vJFHLnyEtg3aAnAo\n4xBP/vAkb8a/SZ7NY+Un9WlWpylm4Q+8suwVJi2bRFJ6Eh0bdmRUp1GEBoby71//zS+JvxDkF8TF\nZ11M/eD6LNu9jA3JG/A3/nRq3AmXcfFb0m8czT4KOL1EhXtrQvxDCPALKDWxCnAFMPjswcz/fX6J\n8zqVt5ByWXNkuYyLVvVbseGukuvVKrqAc647ly2HtrB2/1pW719Nwt4Elu9Zzo4jOwDnG48lTaVQ\nWLBfMO2i2xHgF8DKvSvJzMukeZ3mXBh7IdnubL7d/C2p2am0iWrD6K6jCQsI4/1V77Nk5xLCA8O5\no+sdjL9gPPvT9vPqsld5b+V7ZOVlcWPHG3l2wLM0q9MMcH6HJi6eyJTlUzDG8HDvh5lw4YRSe/m2\nH97OA/99gJnrZtKxYUc+GvpRmb1aIqeqZiZWERE2vmvReawYPhzuvBPS02FI8Tk1GDXK2ZKSYFgJ\n3xYZMwZGjICdO+Gm4nNqcP/9cPnlsGED3F58Tg0eewwGDoSEBBhXfE4Nnn0WevWCJUvgkeJzCTFp\nEsTFwfz58HTxuYR469mRzokAAB6rSURBVC1o0wbmzIEXi88lxLRp0Lw5TJ8ObxSfx4qZM6FBA5g6\n1dlONHcuhIbC66/DjOLzubBwofP6wgvwVdH5XAgJgW+ceax46ilYUHQeK6KiYJYznwsTJsDSovO5\n0KwZfODM58K4cc5nWFjr1jDFmc+F0aNhY9H5XIiLcz4/gJEjYVfR+Vzo2ROec+ZzYehQSC46nwsD\nBsBfnflcGDwYMk5YE+2yy+ABZz4X+vWjmFrwu5faogm33taIO38svl7cmBFh/PLUXsI/+9qj3z0L\n7ElNZMvhreTm5fL+cyMYf/GTtJmxoMTfveS5s3hu0XMEvDyZS37LpX5ofZpFNKVeSD1MSCi7p7/D\ni0tf5J7rJlE3w7IpNozG4Y2ICm3AvsAcrr3OxfI9y3l+vmFQUiQRgXXIzsvmYEYyW8JyuPXaQLo0\n6cID03fRdMsBMgtN6bAxCm6/4tjH8CW0Pvar4+fyI8+dR0JjuHews2/aLGh2Qq61tDk8MvDYxzAd\notKd5CiucRzB/sH4X/wHXI8/4Zxw7HcvN3+OLHceX7WGF3s7h79/13lWnaA6/JDQ2dl5wu9e4WsB\npsbBe50hKg1mz3TRPro9ue4csnKzyMzNYna/hrzbJp2cbVv498zj01zkLyX0zx55zGkDrZPgrRLW\nUX66D3x3lmHgkQY8MtuZUiPQL+DY1BnwQN8svmuSycV7w5j0YxjB/sGk5aRxKOMgbmuZdN0ZXHjF\n3Vy/NxqeeZq9R/eRkpWCyxgahTci4O1/c2aPwdgvvyTluSfYnZLIgfT9ADQKa0zE9M9o2r5Hif/u\nZeVl8cSd7Xn592n86VfLI783JTYyFlfhXlL9u+f8XBv+3cv/b3kaeJpYlT8piIj4rOlrp2PLWRvv\nVjxbdNjgfFswOiyaHUd28sX6L5i6cQZv7OjIiExDZHDdIrMpRYVG8cIfXiA1PpzkPVNJTE1kVfpq\ngvyDqF+/KTmZh3jxDy+Sc/VBjixegIsj/H5wC78f3IKNqs/w9uN57MLHqLt+Ipl7EziU4fTChAWG\nckZkDEPO7sLaA2vZmbKLqFynBsrP5SIrN7vUNuQnLhXhtm5W7HGG1b5buJR/BU0mKiSKqTv3E5br\nws/lR52gCA5nHjmWBLgJcAVgTC4PrqtLgCuQLYe2YLH8um4m33+9Fpue9v/t3XmU1OWZ6PHvU1Vd\nW6/0Qq+sIkZIEO12wQUYl7hGcLmaxbk6OZM4d64eIslxknvPuZPcnBkzc0a8uZHxxCTK6Mw1KgMo\ncYUzGqOoCIo6LKIILd10Q3dD0130Vl313j/equqqXgvosqqrn885v1P1W+v9/eDow/M+v/flntbd\nhMMh/Dk+OvsCDC6JCofDCVO9iAi7Wlo5UA5Th4wdZhAkUic2+nQ2bqebPE8eee4uekN99IWC9IWO\n43F5qK2qo2x+DbndH3LkhK2t87jcVOVXUegt4vb51/PYvpd5dfN/8JO2MH63n9lTZlORV4HbmcNB\nRw4P/OkBvnhxNbc3NeJ0OKnOr6GmoNq+/VgwdMLpzr4AjR0NHD5xhMd3bOW/XvJdHig+m5K250/2\nj0qplMqsjJV2BSr1pUqmdic6yvPJinb9PPzew7T3tON1eZlfNp9Hb3iU86rOG3J8b38vz3/yPI/t\neIxX971K2ISZUzwHr9NLyISorazl7tq7eeOLN1i7ay0fNNu3C6cVTOPKWVcyt3QuHb0dvNPwDm8d\nfIu+UB+CUOwrptRfyhTvFHa17KKjb+QaqmQ5xBHrSjTGjFgAHj3WIQ47sKaAMYaQCTHSf3tFBEES\nPmHgvJGK68EO3Op2RQr5+3uHdPPl5uTGppXp6O2ItdshDvLd+fZlALE1d9FzK/IqmFU0C6/LS1tX\nG7tadtFv+nGIgwuqL+DSaZdS4i/h4PGDbN6/OTaS+NySudxy9i3cNv82FkxdwMdHPuYPe//A+j3r\nYyPQXzr9Uu46564h9WBRR7uP8szOZ2Jdvf4cP99d+F1WLlrJrCmnPvSFUqci7V2BIvIYcANwxBiT\nVMe3BlZKfblOtXYnWSPNjTe3ZC4rL1rJsq8sG3buvsOBw6x4eQVP73yaRTYRxdvT7ee3v/ptfvZn\nP8PtcPPKvld4ed/LvLb/NY71HANsoDV7ymy2HNxC2ITHrCH6Mjlw4HA4EgImIBZkDd5mMIRNeNRg\nKsolLjwuDw5xEDZhevt7h0z743a6KfAUkOPIIRgOcrznOMFwMLa/xFdCeV45Xqft2mvoaIj93fC6\nvJxXeR5zpswh151Le0872w5ti81vmJuTy+IZi7n6jKu59sxryc3J5bUDr7H5881s+nxTbFLkC6sv\n5NZ5t3LrvFuZWTRzyH0c6z7GC5++wLO7nuWlT18iGA4yv2w+3zvve9y58E6KvEVJPm2lxlcmBFaL\ngQDwhAZWSmWmzt5OqldVDzvdS747n0M/PDRsJiEZhzoOUf3Q0C6deIJwYc2FfGPuN7j6jKs5t/Jc\nHOJIOPe1x+2xf/YXiedW5lVy2YzLWFSziLrKOlxOF+82vMsb9W+wfs/6YbNITrE1RiMFW5V5lTQH\nmkfNQI2X+KxUtD1OcSaVBRuOz+XD4/LErtEX6qMr2DUkKPM4PRT7islz5yEIPaEeWk600N0/UItT\n4CngzOIzqcirwOfy0d3fTX17PXva9sSmJirzl7Fo2iIurrmYi6ddjNvl5oOmD9hycAtvfvEm+9v3\nA3ZewCtmXcG1c67lmjnXUJlfmdAeYwx7Wvfwyr5X2Lh3I2/Uv0F/uJ+aghpum3cbdyy4g4UVC3Vc\nKpV2aQ+sIo2YCfxBAyulMtd4vBU4nDvX3znm1DN1VXVs3LuR9w69B0Cpv5QrZl3BgfYDsWENhgus\nLqy+kFlTZrHl4JbYG24uh4uvTf0aue5ctjZspS88ci1VvGgX3Tnl5+ByuGjsbIxlV+I5xYnH5aEr\nOPSNwFMRDawcOGKZJZe4Ylmqkw2s3E43/hw/HqcHt9ONiBAKh+jp76GjtyMhMwX2Lceq/CpK/aXk\nu/NxOpz09PfQ2tXKgfYD9IYGiv2r8qtYUL6AcyvO5axSO5J764lWPjryER80f8CO5h2xAUyn5k7l\nkmmXcNn0y1g6cykLyhfEiubBBlIH2g/wx/o/8sf6P7L5882xiYbnlc3jxrk3svwryzm/+vwxpx5S\n6ss0YQIrEfk+8H2A6dOn19bX16esPUqp4cWPcTTcGEin4sLfXMjWQ1tH3H9R9UW8/Zf2jarmQDOb\n9m1i8/7NbNq3KWFevOECq/hzD3UeYmvjVrY2bmXboW28+cWbCdmXwa6YeQVLZi1hyxdb+PzY5/Zt\ntp5jQwImj9OD1+Ulz51HeW45ToeTL45/weETo48yP5Jo/ZNLXLZGK66G6njvcQAKPYUDGStjCBMm\nFA4RMiGCoWBS3ZpOcVLoLSTfnY8/x2/fUnTYgC0YCtLZ10lbV1vsN6PcTjezimZxZsmZzC2ZS5m/\nDK/LSzAUpKGjgb1H97KrZVcskI2295yKc6irrOP86vO5oPoCZhXNSsgudQe7+aD5A95peId3Gt7h\n7Ya3Y4FUsa+Yy2ddzlWzr+LrZ3x92K5BpTLFhAms4mnGSqnsMVbG6s5z7mTN8jVDthtjuPnpm9nw\nyQZg+MBqZtFM/qr2r1hYsZBzKs6hPLc89j/z32z/DSteXjFqcAW2YLumoIaZRTOZVjCNEl8Jvhwf\ngtAb6qWzt5O27jaaAk00B5o5HDg85jVHIgiVeZUU+YrAkJCNMsZQf9z+g3JG4YyEoCQ6snxkJdZF\nGAqH6A/30x/up6e/h+5gN4FgYMTfdzvdlOeWU5FXQVV+FSW+EvI9+XhdXgShu7+b9p52DnYcpL69\nnvrj9bEuP7D1U3NL5nJ22dnMK53HgvIFLChfwPTC6QntPdp9lI8Of8SO5h2xTNaull2xa00vnM6i\nmkVcNv0yFs9YzPyp8zUrpSYMDayUUmk1Vo1V0w+bhi1cH3zucIFVTUFNLOsBNvNxdunZzCubx6yi\nWfz8jZ8PGwTl5uSy/pvraexo5PNjn7O/fT/17fV8cfwLGjsbE4IJsMFXmb+MstwySnwlFHgKeOnT\nl4YUhcPo9VuCUJVfRX+4n95Qbywo6g/3JxSnx94gFAcuhys2wbLb6cbj8uBxevDn+GP1VB6XB6/T\ni9vlxu1w43LYbBhih2HoC/XR1d9Fe3c7bd1ttHS1cOTEkWHvszKvkumF05lRNIOZhTOZPWV2LHtV\nmVcZC6BC4RAHOw7yadunfNL2CXta97CzZSe7W3YnZPMq8io4t+Jczqs8j/OrbDZrcH2VUhOJjmOl\nlEqrqoIqVl+3eti3Aldft3rEoGrwuT+4Zui5f33+X8eyIx8d/oidR3ayu3U363avo627bcj1HOLA\nKU7uWHAHrSdamVM8h6Uzl1KZV4nH5QFswNAUaKKxo5GGjgaaAk0cDhzm8InDtHS10HKihb1te/G7\n/cOOzj5aN12uO5dgOBirg8px5uAUJ06HE4c46Ana+iRvjjc2rEI08AqGgjZA6u6iN9RLT39PUm8J\nAhR5iyj1l1LmL2N64XRqK2spzyunPLecyvxKqvOrqS6opjq/mhynncg5GArSHGimsbORg8cPsu3Q\nNurb69l3bB+fHf2MA+0HEuq18t35zJ86n+vOvI55ZQPZrNH+fJXKZql8K/ApYClQChwG/tYY87vR\nztGMlVLZpznQPOz8d6k6t+VEC5+0fcLHRz7mhb0vsP/Yfrr6u2Jde4NNzZ0aCzAqciuoyKugLLeM\nMn8Zpf7S2DhYpf5S/Dl+RISO3g4e/+BxdrfsZmruVBZNW0QwHCTQF6C1q5UtB7fQ1NlEgaeAM4rP\nIGxs9qgv1EcwHIzVS4XCA+NSmcjgnfEZK5fDRY4zB7fDZqzcTjdelxefy4cvx4c/x0++O588dx75\nnnwKPAUUegqZ4pvCFO+UWNF4d7Cbtu42Wrtaaetqs9mrEzZ7deTEEZoCTRzqPERDR8Owb0UWegqZ\nPWU2c4rnMHvKbJvNKrbZrKr8Kn1jT00KGdEVeLI0sFJKDbF5s/288srTvlSgL0B9ez0HOw7GAomG\njgYaOxtp7GikOdBMS1fLiBkht9NNsa+YIm8RhZ7CWJF4njuP3Jxcct25sYJxn8uH1+WNdeNFu/Vy\nnDl2FHhxxoKo6ICZtZW1sRqqaOAVDAdjQVl06envidVWdQW7OBE8wYngCQJ9AQJ9AY73HOd473Ha\ne9o51n1sxNqw6ACqlfmVVOVXUZ1fzbSCadQU1FCVX0VNQQ0zimbo2FFKoYGVUipbROcz+5LmBAuF\nQxztPkpLVwtHu4/S2tVKa1crR7uP0tbVxrGeY7T3tNPe005HbweBvgCdfZ0E+gJ0Bbtiww58WaJ1\nV7nu3FiQV+ApiAV/xb5iin3FlPhLKPWXUuIriX0v9ZdGprdRSo1Fa6yUUuoUOB1O2xWYW3ZK50dH\nPe/u76anv4dgKEhvqNd2A0bqpaJF69Epala+shKD4aGrH4plsZzijHUHRgvYo4vX5Y0t8WNEKaXS\nTwMrpZQaRw5x4MuxNVDJina1XT7r8lQ1Syn1JdEBRJRSSimlxokGVkoppZRS40S7ApVSme3Xv053\nC1Lu1zdk/z0qNVloYKWUymxnnZXuFqTcWaXZf49KTRbaFahSxxhYv95+JrNdqeFs3GiXLLbxk41s\n/CS771GpyUIDK5U6GzbAzTfDffcNBFHG2PWbb7b7lRrLgw/aJYs9+PaDPPh2dt+jUpOFdgWq1Fm+\nHFasgF/+0q4/9JANqn75S7t9+fL0tk8ppZQaZxpYqdQRscEU2GAqGmCtWGG36/xiSimlsox2BarU\nig+uojSoUkoplaU0sFKpFa2pinfffRAOa2G7UkqprKOBlUqdaFAVrakKhwdqrm68UQvbVXKefNIu\nWezJm57kyZuy+x6Vmiy0xkqlzoYNA0FVtPsvvubq+uu1sF2Nbdq0dLcg5aYVZv89KjVZiMmgLpe6\nujqzbdu2dDdDjRdjbHC1fHliTVV0+7JlsHLlQHAFWtiuhnr6aft5++3pbUcKPf2f9h5v/2r23qNS\nE52IbDfG1I11nHYFTnanM4hnKAQ33WQ/k9k++PobNsCqVYnbV62y28cK+HXw0cnjkUfsksUe2fYI\nj2zL7ntUarLQwGqyO51BPG+91e6vqBgIokIhu75hA1xyycjXvuUWu9TWJl6ztja5GisdfFQppVQG\n0sBqsosfxDMapCRb67R2LZSWQmvrQHBVUWHXS0vhrbdGvva998LChbBjh/0MhRLXly1LXbuVUkqp\nFNHi9cnudAbxdDqhuXkgmHJF/jqVltrtTufI1168GH71q4Fgyum0+6Lrzz1nuxNT0W6llFIqRTRj\nNdmFw/DjHw+di+3BB+32YHD0Oqr166GpKXFfUxM8/7zNIo00QOjy5XD//TD4ZYVt2+z2sTJWoIOP\nKqWUyjiasZrsfvIT+Md/hMceS9wezUKtWweffWbXo1mo+C6/DRvA6008Nz8fenrsucuXDz9A6OLF\n9ndffTVxX12dzVhddNHoGSsYefBRDa6yy9q16W5Byq29LfvvUanJQjNWk93f//1AnVRpKfT3J67v\n3Dl6HVVOjg2ivF6b3fJ6B9ZvuGHkAUJff/30aqxGG3w0vqBdTXylpXbJYqX+Ukr92X2PSk0WmrGa\n7J5/fiBIGlwn1doKL7wwch3VokWwceNAMJWTY/dF1y+9FLZuHXmAUDj1GquxBh9dsmTsjJeaGNas\nsZ933ZXOVqTUmh1rALhr4V1pbYdS6vRpxmqiOJ1xm8Jh+Ju/sZ+Dt7/1FpxxBjQ0JO5raIA5c+DK\nK6GgAA4cSNx/4ABs2mQDrba2xH1tbeB2226+igrb5RftmhOx6+Xl8MMfnnqN1bJl9rhVqxKvvWpV\n8jVaamJYs2YguMpSa3asiQVXSqmJTQOrieJ0xm2K1lHV1g4EV+GwXX/wQdi3D3y+xHN8PltbVVgI\nXV2Ql5e4Py/PZqX6+yE3N3Ffbi709UFxsc12+f22mxDsp98Phw/b364bNIhtXZ1t63PPjf48nnvO\nHrdyZeLzWLkyufOVUkqpFNDAaqI4nXGbHnhgoIstGlzV1tr1BQvsMdE3+Hp77Wd0fXA2KhAY+Xd6\nehLXjx8fKHb3+WxQ5fPZdYfD/raOY6WUUiqLaI3VRHE64zY5HLB9+0AwFV/PdNVV8NFHA8GUxzPw\ne8bABRckXmtw5ire4LcDN22C7u6BYMrtttudTnjqKbjtNh3HSimlVFbRjNVEcjrjNkWDq3jbt8Mv\nfmFrkgZnm3p67PZdu2z2Z3CmKhCw2599dvhzo0Mt5OTY4Cped7edDmfduuHbFD13LDqOlVJKqQyj\ngdVEMtK4TeHw2IXt0e6/eNH1v/s7W0sVr7DQbne5bGZpuBqrm2+Gf/iHoZkqr9d2P4ZCA91/8Xw+\nW5u1fLmtiYq3cqXdnkxwNNLz0KEWssuLL9oli734nRd58TvZfY9KTRrGmIxZamtrjRpBOGzMihXG\ngP2MX7/++sTtg49fu9aYhQvt94ULjQmFBtYXLDDG47HfvV5jgkH7GV1/4gn7Pbp0dyeuxy+9vYnr\ntbXGOJ32u9NpTF9f4vo99wx/P/H3cSrPI5nzlVJKqZMAbDNJxDJpD6biFw2sRrFu3ejB0+DgKj7I\nuP/+xKDKmMTgKj6oMiYxuBIZOObuu+217757aFA1OCiLX6JBlTGJwdVo97Nu3ek9j7HOVxPH6tV2\nyWKrt642q7dm9z0qNdFpYJVtwmEbLAzOxES3h0IDQcXgoCUUssFVNKiKCoWM+dGPjDn//IGgKioY\nNOaCC4zp7DTG7x8aTN19tzE+nzHFxUODKa/XmKlTjQkEjJkzZyCoiurrs9ufeWbk+0kmYzXa89CM\nVfZYssQuWWzJ40vMkseXpLsZSqlRJBtYiT02M9TV1ZltgweMVMkzxhapR4XD41fIPdq1+/sHRl0H\nW1fl0hdO1ThZutR+vv56OluRUkvXLAXg9bteT2s7lFIjE5Htxpi6sY5LafG6iFwjIp+IyGci8uNU\n/takZ1JYyD3atfv77aTL8fLz7XallFJqkklZYCUiTmA1cC0wD/iWiMxL1e9NatHAJxUTEo927Xvv\ntUHUcJMwa3CllFJqEkplf80FwGfGmM8BROT3wDJgVwp/c3JK5YTEY10bbDDV2Wm7/zo7B4KtSy6B\nd989/ftTSimlJoiU1ViJyK3ANcaYv4ys/zlwoTHmnkHHfR/4fmT1q8B/pqRB2acUaI2ulEBRG7QP\nPmik7SdjtGuXQ8Uu2DN43zz4ynDb0yThWalR6bM6Ofq8kqfPKnn6rJL3ZT6rGcaYsrEOSnuFsTHm\nUeBRABHZlkxhmNJndTL0WSVPn9XJ0eeVPH1WydNnlbxMfFapLF5vBKbFrddEtimllFJKZaVUBlbv\nAWeKyCwRcQPfBJ5P4e8ppZRSSqVVyroCjTH9InIP8ArgBB4zxuwc47RHU9WeLKTPKnn6rJKnz+rk\n6PNKnj6r5OmzSl7GPauMGiBUKaWUUmoiS+kAoUoppZRSk4kGVkoppZRS4yQjAiud+iZ5IvKYiBwR\nER3vawwiMk1EXhORXSKyU0RWpLtNmUpEvCKyVUQ+jDyrn6W7TZlORJwi8oGI/CHdbclkInJARD4W\nkR0iopPBjkFEikRkrYjsEZHdIrIo3W3KRCJyVuTvVHTpEJEfpLtdkAE1VpGpb/YCVwEN2LcJv2WM\n0RHahyEii4EA8IQx5qvpbk8mE5FKoNIY876I5APbgeX6d2soEREg1xgTEJEc4E1ghTHmnTQ3LWOJ\nyEqgDigwxtyQ7vZkKhE5ANQZY3TAyySIyL8AfzLG/DbyRr3fGHNagzxnu0gc0YgdhLw+3e3JhIxV\nbOobY0wfEJ36Rg3DGPMGcDTd7ZgIjDFNxpj3I987gd1AdXpblZmMFYis5kQWfbNlBCJSA1wP/Dbd\nbVHZQ0QKgcXA7wCMMX0aVCXlCmBfJgRVkBmBVTVwMG69Af2fnxpnIjITOBfQyQtHEOna2gEcATYZ\nY/RZjez/APcD4XQ3ZAIwwKsisj0yhZka2SygBXg80s38WxHJTXejJoBvAk+luxFRmRBYKZVSIpIH\n/DvwA2NMR7rbk6mMMSFjzELsLAkXiIh2NQ9DRG4Ajhhjtqe7LRPEpcaY84Brgf8eKWdQw3MB5wGP\nGGPOBU4AWnc8ikh36Y3As+luS1QmBFY69Y1KmUi90L8D/2aMWZfu9kwEka6H14Br0t2WDHUJcGOk\nduj3wOUi8q/pbVLmMsY0Rj6PAOux5R9qeA1AQ1y2eC020FIjuxZ43xhzON0NicqEwEqnvlEpESnI\n/h2w2xizKt3tyWQiUiYiRZHvPuzLJHvS26rMZIz5iTGmxhgzE/vfq/8wxtyR5mZlJBHJjbw4QqRL\n6+uAvtE8AmNMM3BQRM6KbLoC0JdtRvctMqgbEFI4pU2yTnHqm0lLRJ4ClgKlItIA/K0x5nfpbVXG\nugT4c+DjSO0QwP8wxryYxjZlqkrgXyJv1ziAZ4wxOoyAOl3lwHr7bxxcwP8zxryc3iZlvHuBf4sk\nGj4H/iLN7clYkWD9KuDudLclXtqHW1BKKaWUyhaZ0BWolFJKKZUVNLBSSimllBonGlgppZRSSo0T\nDayUUkoppcaJBlZKKaWUUuNEAyulVMYQkZ+KyI8i39eIyK2neJ2ZIjLqeEmRY74dt36XiDx8Kr+n\nlFJRGlgppSarmcC3xzpIKaVOhgZWSqm0EpH/KSJ7ReRN4KxBu2siAyWOdO5PReRJEXlbRD4Vke8N\n2j87kpn6k4i8H1kujuz+BXCZiOwQkfsGnXd95JqlIvINEXk3MinuZhEpH4/7VkplJw2slFJpIyK1\n2GlhFgLXAefH7fYBNwP5Y1xmAXA5sAj4XyJSFTn3DOBS4AhwVWQi4NuB/xs578fAn4wxC40xD8W1\n6abIvuuMMa3Am8BFkUlxfw/cf+p3rJTKdmmf0kYpNaldBqw3xnQBiMjzkc//gg2KVhhj2sa4xnPG\nmG6gW0ReAy4CvgfsM8Y8ISKFwMMishAIAXNHudblQB3wdWNMR2RbDfC0iFQCbmD/qdyoUmpy0IyV\nUirjGGOeBTYle/ig9RDw3+LW7wMOA+dgg6YRuxaBfdgMWXzw9SvgYWPM17BzknmTbJdSahLSwEop\nlU5vAMtFxCci+cA3TuEay0TEKyIl2AnK3xu0vxBoMsaEsZNyOyPbOxnazVgP3AI8ISLz485vjHy/\n8xTap5SaRDSwUkqljTHmfeBp4EPgJYYGRQCIyP8WkRtHuMxHwGvAO8DPjTGHBu3/Z+BOEfkQ+Apw\nIu68kIh8GF+8bozZA3wHeFZEzgB+Gvm+HWg9+btUSk0mYszgLLpSSk0MIvJTIGCM+ad0t0UppUAz\nVkoppZRS40YzVkoppZRS40QzVkoppZRS40QDK6WUUkqpcaKBlVJKKaXUONHASimllFJqnGhgpZRS\nSik1Tv4/EcuC10H+HqAAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n", + "draw_means(fig, X_mean)\n", + "plot_prob(fig, X_mean, X_std, classes)" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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2pSyP707xOgBg7DBLhKfrr++7/Prr+4aqTE0ws62TCmugaSadc87gxeOp5bnGlqvAupDx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\nAsMVKwAAgIBwxQoAACAgBCsAAICAEKw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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n", + "plot_decision_boundary_bayes(fig, X_mean, X_std)" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Przygotowanie danych dla wielomianowej regresji logistycznej\n", + "\n", + "data = np.matrix(data_iris_versicolor)\n", + "\n", + "Xpl = powerme(data[:, 1], data[:, 0], n)\n", + "Ypl = np.matrix(data[:, 2]).reshape(m, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = [[-22.4168027 ]\n", + " [ 12.03703048]\n", + " [ 11.13804517]\n", + " [ -1.75684025]\n", + " [ 1.01230657]\n", + " [ -7.61403096]]\n" + ] + } + ], + "source": [ + "# Uruchomienie metody gradientu prostego dla regresji logistycznej\n", + "theta_start = np.matrix(np.zeros(Xpl.shape[1])).reshape(Xpl.shape[1], 1)\n", + "theta, errors = GD(h, J, dJ, theta_start, Xpl, Ypl, \n", + " alpha=0.05, eps=10**-7, maxSteps=100000)\n", + "print(r'theta = {}'.format(theta))" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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wKJCIiLolOtwVHWKLLtH3yYa7rB4qix3+i21bKJR8qC7Z8TO9fy47je+OFIcCMx6mYhcG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\niCbz1X9Yj5qnajDoO4PY+02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NcsE92A3PUCMIe4Z64B7qhmsgex+JrMahwL4gXoF37CSb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\niIiIyCT/H+AGYmKcYPyGAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(Xpl, Ypl, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n", + "plot_decision_boundary(fig, theta, Xpl)" + ] + }, + { + "cell_type": "code", + "execution_count": 55, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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SlFgfnliCx6OXcNp3f5vxl3dfxeUe4+kpLs92KI6l8+1O2pa3EX4lTOuLrXSs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\nUPf5OjZfu5n1l62n7LtlTPmPKYw6Z5S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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(Xpl, Ypl, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n", + "plot_decision_boundary(fig, theta, Xpl)\n", + "plot_decision_boundary_bayes(fig, X_mean, X_std)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Kiedy naiwny Bayes nie działa?" + ] + }, + { + "cell_type": "code", + "execution_count": 56, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Wczytanie danych\n", + "import pandas\n", + "import numpy as np\n", + "\n", + "alldata = pandas.read_csv('bayes_nasty.tsv', sep='\\t')\n", + "data = np.matrix(alldata)\n", + "\n", + "m, n_plus_1 = data.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data[:, 1:]\n", + "\n", + "Xbn = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n", + "Xbnp = powerme(data[:, 1], data[:, 2], n)\n", + "Ybn = np.matrix(data[:, 0]).reshape(m, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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D67dLqoTXXxzuv17S9eHjXLXScxLAIRMIxjqjVrsyCMrD6xY/EUQniPrbANKT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\nzP8Pwi7E6dNciUEAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(Xbn, Ybn, xlabel=r'$x_1$', ylabel=r'$x_2$')" + ] + }, + { + "cell_type": "code", + "execution_count": 58, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "count: {0: 69, 1: 30}\n", + "prior prob.: {0: 0.696969696969697, 1: 0.30303030303030304}\n" + ] + } + ], + "source": [ + "classes = [0, 1]\n", + "count = [sum(1 if y == c else 0 for y in Ybn.T.tolist()[0]) for c in classes]\n", + "prior_prob = [float(count[c]) / float(Ybn.shape[0]) for c in classes]\n", + "\n", + "print 'count: ', {c: count[c] for c in classes}\n", + "print 'prior prob.:', {c: prior_prob[c] for c in classes}" + ] + }, + { + "cell_type": "code", + "execution_count": 59, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[matrix([[ 1. , 0.03949835, 0.02825019]]), matrix([[ 1. , 0.09929617, 0.06206227]])]\n", + "[matrix([[ 0. , 0.52318432, 0.60106092]]), matrix([[ 0. , 0.61370281, 0.6081128 ]])]\n" + ] + } + ], + "source": [ + "XY = np.column_stack((Xbn, Ybn))\n", + "XY_split = [XY[np.where(XY[:,3] == c)[0]] for c in classes]\n", + "X_split = [XY_split[c][:,0:3] for c in classes]\n", + "Y_split = [XY_split[c][:,3] for c in classes]\n", + "\n", + "X_mean = [np.mean(X_split[c], axis=0) for c in classes]\n", + "X_std = [np.std(X_split[c], axis=0) for c in classes]\n", + "print X_mean\n", + "print X_std" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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6dEX3ut3RvW53nl+sPEilwKJFwIoVLIn2sWMsxlWBFBcDZ6pviohZETDRN8GT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\nrkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(Xbn, Ybn, xlabel=r'$x_1$', ylabel=r'$x_2$')\n", + "draw_means(fig, X_mean, xmin=-1.0, xmax=1.0, ymin=-1.0, ymax=1.0)\n", + "plot_prob(fig, X_mean, X_std, classes, xmin=-1.0, xmax=1.0, ymin=-1.0, ymax=1.0)" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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37voxQn5f3HJS7flohWR7TgoEFWUVeOTjj2DJrCWWdsMHgCvDv/fvMoAR9cIA\nRpRD75oBrBBGwKKv5ksVXqzYdghIvC1QvK8/80wkfO3dG7niMbpxqxmQojfljr0wwBQvLCoVaQoL\nRGqIrie2tnj7RiqFG//l12ic9RTWf+qHWHPDaqyf/Pdo/Pp5owVF+DGeR7+Npz9fi/bwlZKxrLri\nMJm+7DnZV9Xl5RjvdHa/ESGiCK4BI8qhg+3tsCuFyRUVuktJ3BIiXnjp67ZD2TCDzsKFkV5f5vPP\nn29MYZo1xl7FGO9KwwT9uzLunp9k7Vv1os8jUbcss8u9Oe0Xj5VXHCaSrA1FPp5/usvV/UaEiCI4\nAkaUQ+91dGBqZSXKC+UKyOgQZkrWvyudkSYra4ueooz23HORLvmJmsHGTotmMuJnMXPdlcfngS8Y\nf/oRsPaKw0SSbdydj+e/oqoKhzo6ECrCXVeIcqlAzgpE/dN7HR24ohDWf5nSDS9A/LA2Z078Y1q5\niD9ZjXEWxPcKWbH15zNEhiVbdwUAzjIn3A63pVccJmK2oXA73HDZjalwl92Vt+e/sqoKnaEQjnd1\n5fR5iIoNAxhRjvhDIRzp6iqcAJYsvNxxh3E7WijU+4rEu+8Gli/v27qwbGtcscIIevGawcZeuWhK\nd8TPYsnWXQHAzRNvtvyKw2RuHH8jGh9oxPp563N2xWMiZvuJQ53xNwMnKlVcA0aUI0e7uhAQKZz+\nR4k62dfXG4vfFywwpvqUMoLP7NmRxe/PPWcEryeeiPTNevxx66f0UnXbnzMns2awme5daZFU667u\nvvLunI48JWr6auWek+maVlkJwNgT9RPcE5IoQkSK7mP27NlCVOi2NjcLduyQP7S06C7FEAqJbN5s\n/DdaMCgyf74xwbdsmXG/ebu21rjf/P6lS82JwMiH+T1W1JXO5+n+bNH1Ll1q3F62zJqaU2jtahX3\nw27Bt9Drw/2wWzxeT86ee1fDLnE/7BbXQy7BtyCuh1ziftgtuxp25ew5kwmFQlKzc6d89dAhLc9P\nlG8AdksaWYZTkEQ58n54yuXyQhkBS9QSwmYzRrii10pt22aMfO3ZE1n8rpQx6rVpU8/v7+toUnTL\nCyByxWH01Gai2k1bthiPjZ4e3bIlMlo3Z07q6UoLZbvuyuP1YMNbG7D6pdXY8NYGeLyejJ43evG/\njqav8SilMLWyEoc5BUnUA6cgiXKkvrMTg8vLMdhu111KavE2qDanI2Pt3Nnzdl+n9KxseRE9PfrK\nK73vN3/OOXMiY3g5moo0111t3L8R9RfqMWXwFCyesThh+DLbVvRlu6KN+3+VuOmr34eN+3+FJbP+\nJuufKVtTq6rwemtr3p+XqJDtPuvYAAAgAElEQVRxBIwoRw53dGBKeP1LwUvn6shMrkDMhBVXK955\nZ8+9HW024Ac/iNy/c2fP+nbuNC4oyOEoGABUO6qxZNaSlJ3mrRq5Ovz69sRNX8WL+j9uz+4H6aOp\nlZVo6OqCL/ZCD6ISxgBGlCP1nZ3FEcDSDVaJFshbMaXX16sVzelRM4SZ7r8/ss9jnnuBZSJZ24p0\ntisypy731XTCIfH/WXdJOaZ85PY+15qNyZWVCAE4xlYURN04BUmUA75QCCe83uIIYKmuPJw71xhh\nMjvVp3sFYiZydbWiWZ9Sqbv/a9SX7YJipy6R4EeyOSuxeMafW1Fuxsy/g/rOzsJZE0mkGUfAiHLg\nWFcXQjDe+Re82L0ORYxQtnZtz02pE0m1QD4VK6Y2RSJtMqKZI19r1/b8egGFLyDStiKeZNsFxZu6\n7BZ+2VxeGIv/x61BdYLnyDVzK64jXIhP1I0BjCgHjoZPNJMKYQ/IVGIDlHlV4sqVkdEuqxuuRrNi\najP6iselS40QF70mbMGCno/vy5q1LCW7wjGr7YJEsPHnqxNOXTqDwCffB9Y/DzRumoAbv/Rgzte8\nJTLC4UCVzYajnIIk6sYARpQD5olmUjGMgMXK9x6KsSNwQCSEpTMCF23pUmMtmLkm7P77ja9v25bW\n6Fpf20Ak8trx1zBm7Rgsf345Hvv9Y1j+/HKMWTsGrx1/DUCWbSueeQaHN/444dSltxy45q9WY4nU\nonrPO0BtrfHzxwZPq7eSikMphUmVld1vTIgIUFKEG6TW1dXJ7t27dZdBlNDXjhzBD06eRMecObAV\n0FRXUubUoxl4zNBlig43fTl29Pcn+rpVx9+82bjaMbr26EC5eXN337F4bSBsypZRG4h4PF4Pxqwd\nA4+vd5hzO9xofKCxO2C1+drSblsBEWxYfSuWl/8O7c7ed7u8xujXkj/BCF979xp3RI80JngtcmHB\nO+/gWFcX3v7Qh3L2HESFQCm1R0TqUj2OI2BEOXCsqwuXVVQUT/gCejdEjb0qce7c7ENS9LFzsY9k\nonVod95pBIvo4BhndC2XDUwzucIx3bYV5s+x+NubYXPE7zNnA7D4QPjGnj3w/PoX2PC1m7H6wHps\nWH0rPF2teb0idEJFBY51daEY3/QT5QIDGFEOHOvqwoRiWP8VLXrqcfly4yPaq69mP02Valpz4cL4\n02B9nR5LFMxivm5VG4h4U5d9ucIxFXdFDbZ/+Xdwe40RLyA8dSl2bH8KqA73ZH3ta4sxpv5eLB/4\nOh67EVhe/juM+fYAvLYlw35rfXBZRQU8wSAuBgI5fR6iYsE2FEQ50NDVhVlDh+ouIzPmyJBIz6sJ\noxezR7d1yObYQPx2EOYImRXTY1lMd6YOSYcTPl2qDvapNuZOdIVjWkRw47pNaPwxsPEqoH4wMKV6\nMBb/9gSq7zVeS8+Kr+J254/hiWqQb05Z3v4FoPGb30E1YATdXE0RA91vSBq6uopjdwiiHOMIGJHF\nOoJBNPv9GF9sI2CAcZKdO7fn1x5/3Pjoa8PVZM1WrVz4n8V059QGT/cIUiyXF5jSEH8xfjpTl1ld\n4ZiOqNeo+t5lWLInhEcq5mPJsydQPb3WaL2hFDZ+6VqEHPHfa4cAbPzGnZG9NHM1RQzgMqeR+hp4\nJSQRgAwCmFLqVqXUT5RSteHb91hVhFJqnlLqkFKqXim1xqrjEulwwmucycc746yMLnQixlRjtOg1\nYZlelRh77Nhmq3fcYVyZZ8V2RKYswtziLz6aeC2Vw47FX3w07n3pTF1muzF3SvHad2zdamyivncv\n8OyzAIDDF+rRruJP+7U7gfq3fmf8P1+6NKdXvppvSMy/D6JSl8kU5F8DuBfAPyqlBgOotaIApVQZ\ngH8FcCuAkwDeVEptFZF3rTg+Ub6dCL/DL7oRMPOk+8QTkZN69JWQ69Zlf5Vc7Al93TojfG3bBsye\nDezZY4SutWt7XnmZIHx5vB5sPLARh88fxtQhU7H4qsVwO93GnammO+Mcz1xLdfvPbkHI50e70xj5\nsjns2P7l36HaPHaMdNd3Zboxd1ri7UxgsxmbqEddzZpyCnTWR4DvPwFs2pTTHQOG2e2osNlwnAGM\nCEAGbSiUUk+KyD3hzx8FcIuI9Pl6YqXU9QC+JSKfCN/+OgCIyCOJvodtKKiQ/UdTE5YcOoSj112H\nicXUB8ychspFm4J4xw6FjPC1d68xarN1a+S2KU4ASLtdhIgRSEzmSFsSbV4PNl5fY6ylugAs/kNr\nwvAFABve2oDlzy9PGG7Wz1uPJbOWpH59spXGejePry15G4yVp1C9/eXIKFeGr1kmpr7+OmZXV+NX\nV11l2TGJCk0u2lBsMz8RkTUA/iubwuIYA+BE1O2T4a/1oJS6Rym1Wym1u7m52aKnJrLeyfA7/NHF\nNgVpZUPUdI5tsxkjX/PnGyNhZWVG+KqtBYLBuA1T024XkWhvyWRvOEVQvfobWPIn4JHfGf2zqld/\nI+n35Gx9V7rSWO+WcgrU6Y4E60xfswyNczo5BUkUljKAKaXWK6WUiDwb/XUR+UHuyupNRJ4UkToR\nqRs2bFg+n5ooIye8Xgy32+G0Fdk1Lmm2bMj22J7bP44Nf/ppz1YN5pRZNHM6Ms52RGm1i8hmb8ks\n96PM2fqudKW53s2cAl0/bz3W3LAG6+etR+MDjZERQyv240zDWKez+w0KUckTkaQfAL4L4DkAVeHb\nnwDwv6m+L90PANcDeCHq9tcBfD3Z98yePVuICtUn9+2TWW++qbuM3AqFRDZvNv6bxtd3NewS98Nu\ncT3kEnwL4nrIJe6H3bLr2E6RZctEjFO88bFsWeT7Y4636sVVgm8h4ce8n8+TVf/6afnJLEjrsnt7\nHsd8ns2be9e8alXv5w4GRebPj/89MTxej2zYs0HWvLRGNuzZIB6vJ6uXNSvRP1u81zAdmzfHf+0T\nvWZZWnPkiJS/8ooEM6mNqMgA2C3p5J+0HgR8HsCbAP4XwAsAbkrn+9I8djmAowAmAnAA2AfgqmTf\nwwBGhWzmG2/IHW+/rbuM3MrghN3a1Sruh91xA5P7m3bxOKKOY35/ggDxkz0/6Q5x8T4c33EYAe+f\nnUbAa9gV+eZ44TA6fM2fb4QukZ7ha9WqzMKMDqFQzwCWqt7Y18K8HQzG/7pFP/8PTpwQ7Nghp71e\nS45HVIjSDWDpTEHeAuArANoBDAWwVER2WTH6BgAiEgBwXzjYHQTwaxE5kPy7iApXo8+H0Q6H7jJy\nK4NWD0mnDX1+bFx2S2RtWJxpx2jJ1lwBgC9odBttF2/vdWHRU6kS7rC/ZQvw2GPGurNt24yfYdMm\nYNYs4/b8+cCjj+a8S3yfhELGFaXRVqwwvp5oF4HYtWNmL7aVK3v2/bJi+jnKmPC6yFOchiRKaxH+\ngwC+ISIfA7AIwEal1M1WFiEi20XkchGZLCIPWXlsonzyhUI45/cX3wL8TGXQtytpqwYnUH9bXcpF\n/+ZWP9/d+V3cW3cvqh3V3WuunGWJX+uE2wiZAcTsf7V3L3DNNUYLjkWLgH37jFC2dWthhy8RYMEC\nIyzGXrwwe3biJqpWNr7NwKjwG5Mmny/FI4n6v5R9wETk5qjP31FKfRLAJgAfzWVhRMXodPjEMqq/\nj4ABkbCUom9X6q14pvY+blS7i3htJxQU7vvwfVBQ2Ht6L54/8nzcEhPutRgdQJYuNT6it18CIhcD\nFLJnnomEr717jRGstWuNYGm294gXprLolWYF841JI0fAiDLfikhEmgDckoNaiIqe+c5+ZCkEMHPU\nJFqcK+b60qohUduJNn8bfvTmj/DgnAdx9/S7u0fDYiXcazF6BO+JJ3qHL8AIMxa2YMgJs73Hnj2R\nQGm28zB7qyUKU8m2hsqRERwBI+qW1ds7Eem0uhCi/qBkRsAyaFvQl1YN6bSdyDrgxQsgptpay1sw\n5IQ5Wmi27Yj23HPJR/DSDNBWctpsGFxejjMMYETcjJvISmdKZQQs3j6ESRbQp+xDlUA6W/1kHPDM\nBfihELB8ec/75s8H7r8/0hA23c3HzWPGhpdEX7dapmEqgwBttREOR/cbFaJSlslekESUghnAhvf3\nABZvH0IzhM2dG3fdUbWjOuNteVKvHzOmFzPaa9FcgG+umwKAT34SaGqKXPlorglbtSq9BenmMXOx\njVMqsWEq3h6esdOKiQI0YHx97tyc1TvC4eAIGBGQXh+wQvtgHzAqVF89dEgG7tqV+oGUlqQ9xB52\nZ9fwNBSK9PiqrRV5+mmRpUsjtwGRTZsy638Vr4dZip5mlsmmiWqGjXSttHj/fpnyxz/m7PhEuiHN\nPmAcASOy0Fm/HyPsdt1lFC2P14ONBzbi8PnDmDpkKhZftRjbv7A94ebbWW31o5SxON1s37BokfH1\nZcuMKwiffbb35tbpHNPqqwol9Ubb3f27YkcjAWDOHOMjegQv+nvjjXDFXIGaC8MdDjRzBIwISgp5\ngWkCdXV1snv3bt1lEPXyZ3v3IiCCXddeq7uUohOv3YQZtGpH1qY3vZgJkZ6L1EOhvl8BaOUxt2zJ\nflqzL9+bY985dgz/dOwYvHPmwFHobT6IsqCU2iMidakex99+Igs1+3wYxhGwjCVqN2F2sweAJbOW\n4JGPP4Ils5ZYE776cgVgvMX1Ir0X9fdlQXtfmqVqarSaDnN9ZLPfr60GokLAAEZkoWa/nwEsC+m0\nm7CMFVcAxm7lY4Yvs5/Ypk19v6owg90GLP3eHBsa/vvgNCSVOgYwIouICM77/d0nGEpfOu0muvW1\n5UOGLTTiih1h2rIlEr6WLjWm9zI9Zjx9aZaqodFqOsy/j/OBgNY6iHRjACOyyKVAAEEAQxjAMma2\nm4inVzf72NEnIDKqlWjvw2jmovXoMJJgD8qEYkPb3XcbX1+6FHj8ceP+TI8ZT1+mSjU0Wk2HGcDO\ncQqSShwDGJFFzHf0DGCZy6ibfV/XN5lX+sWOBCX6erLjxI4wmeEr22NG68tUabLvveMO43bs4/PR\nMBbAkHLj4vsLDGBU4hjAiCxinlAGl7O7S6Yy6mZfKOubsh1hSncKtS9TpYm+d/58o/XGggXZjR5a\nYLA5BckARqUunWZhhfbBRqxUiJ4/f16wY4e81tKiu5Si5fF6ZMOeDbLmpTWyYc+G5I1WQyFz+bvx\nEQzmr7loXxqvpmqcumqVcTu67nQ+jxYMGscJBnt/3WxCm++GsVFcr74qKw4fzstzEeUb0mzEqj1M\nZfPBAEaF6JenTwt27JB329p0l1I0Wrta5Sd7fiKrXlwlP9nzE2ntak3rvh7BwfyIDRaxj4vXET5b\n2XSfj1d7bAgyf4b58yPhKV4460sd8V67PIYvEZFxv/+9/NXBg3l7PqJ8YgAjyrMfnTwp2LFDmrq6\ndJdSFHY17BL3w25xPeQSfAviesgl7ofdsqthV9L7kgYYcyuhXI/u9HUrn0QhKHqEqrbWuB37s0WH\nqmxH4mJHD/MYvkRErn7jDVn49tt5fU6ifEk3gLETPpFFHm5owIMffICOm25CZVmZ7nIKmsfrwZi1\nY+DxeXrdV22vBhTQ5mvrdZ/b4Ubj1H9D9We+kLjLu7nOyVQAva/ikgRd80MhYPbsyEbhQGTj8Hg/\nS/TPbkr2M2f6+ByY86c/wQbgFe4YQf0QO+ET5dmlQABOpRi+EvB4Pdjw1gasfmk17tt+H4KhYNzH\n+UI++IPxF2iHJISNkzqSt5HYurXnNxVq+Eq0gN9mA/bs6XlfovAFZNbvKzp8ZduE1gIDy8vRwj5g\nVOJ4uRaRRVoCAdQU+RWQ8TbDdjvdfT5u7D6Pdpsd/lD8kOULJu6QbjRlPQLc+Te97zQ3po4XbAop\nhMWGoHXreo5IrV0LrFzZ+/vWrk0eqqIl+pkTXR0JGF+fOzcve0QOKC/HpWD8AE5UKor7bEFUQFqD\nQQwo4gAWbzPslS+sxPYvbMeN429M6xjxAhyA7n0eTYnCFwA4yhxQUPAGvb3u69WUNVqqYFMoISxV\nCKqvN6ZQzWlH0+zZxshY9LRlpj+z2YT205/uPXo4d27e9oisKStDK0fAqMQV79mCqMC0BgKoKdLp\nx+jNsE3m1kC3P3U7Gh9oTLkBdqIAd++H7k24z2M8DpsDUIgbwHo1ZY0WG2wAYM4cI6REj+6IGI+N\nDiH5lCwEOZ3AY4/1XPO1dm1kTdiCBcBzz0W+L9MRLbMxbKxEX8+RAeXluBQIGAuRCyEUE2nANWBE\nFmkNBgt6CjJ6DdaGtzbA442Erb5uhh0d4Mzg1u5vh8fnwbo/rEu4zyMAlCvjNTMbr/72i7/Fb7/w\n2/SaskaL3WLomWciWwRt2mTcb44Y5anpaFyx3fEl3IAVAB59FFi1yghbS5caAVIpY+TLvLggum4r\ntlXSoKasDEEAXbEd+YlKSOGeLYiKjCcQwGUVFbrLiCvV9OKBswfS3ww7jmQBTikFZ5kz4ZTioumL\nMKp6FKYMnoLFMxZ3B6zGBxqxcf9G1F+o73VfgifqOYoTvWWReV/slkWJRsOiQ1HsVkJWj6CZe1ua\no1iPPgpcdx3w6qtGgNy82ajhueciz5voZ0719QLhDr9R8QSDvGiFShYDGJFF2oJBVBfgySTV9OLT\nn30aP97944Tfn3TdVdjh84cTBjhf0AdHmSPufTZlww9v/2HcYFXtqMaSWUuSPm9SsdNx5rqo6Om6\nLVt6hp/Ylhaxj4++zwxGfRUdFAHjuXbuBJ54oufelgUeqjJh/p14gkEM11wLkS6cgiSySKEGsGSj\nU8FQEAt/tTDu6JQp6bqrsKlDpnZPF8Zy2V1Ycd2KzKcUrZCqRUOyjb2XLjU+st30OxlzhE2k73tb\nRh8rna8XAHf476SNV0JSCWMAI7JIWzAIVwEGsGSjUx2BjoT9uACgorwirZC0+KrFsKn4/5z4g36M\nHTAWh+47hPXz1mPNDWuwft56ND7QmPbVlWmLDR3J+m0BycPP448bH7nY9Nucdoyu5aabej5m3Trj\nvtWrjX5diX7O6GOFQsbXQ6Gea90KLIy5GMCIGMCIrCAi6AiFCjKAJRudKlflSVtC/H3d36cVktxO\nYzQrepTL5Av5sOblNZj2w2mYNnQaHvn4I1gya0nfR77ihQozjNxxBxAMRkasamuN++fP7910NNko\nWSZNTjMRO/K2eTOwaFHPxyxfblz1+Nhjxn9jQ6UZrqKPtWCB8fXZsyNhceFC/RcexHCFW2m0M4BR\nCWMAI7JAVygEQeTEUkiSjU6V2cqSTh1OHzY97ee5cfyNaHygEd/7+Pdgt9l73GdeEXn7U7fH3WIo\nK/FGkRYuNMLWtm3GQnYzfJktHbZujYQVM4wkGyVLNYKWrdiRt+jwdf/9xtTnE09E+oFt25Z4GjT6\nWOYWTHv3Gt9nNnW1YtrUQuYblQ4GMCphhXe2ICpCHeEpoqoCHAGLNzplrsHa+rmtCcNZOmu/YlU7\nquEsdyZcdJ9OS4u0xVu/tXJlJHyY2/lEb+Njs/Vs0ZBsa57ly42PXG3bE2907f77gR/8wAhfpn/8\nx9TToPGOtXcvUFZm3bSphcy/kw62oaASpvUqSKXUZwB8C8CVAD4sItxhm4qS+U6+qgBHwIDI6FS8\ntg7bv7C9V4sKm7JlvUA+2ZqzdFpapC3ZVY5r1xrhwxQbVsyrCbdsSd7I1DxeLrbtiTe6FhuQNm0y\nnuOuu3punp1oQ+5ECih8AZG/k04GMCphus8W+wHcBWCn5jqI+sQ8kRRyTyOzrUPsGiwznFm1QD7V\nFZGpWlpkJN7IT7y9FBONWCVrZLppk/GRiyan8UbezGnHaDt3pp4GjT1WMBhZ85bq59ek0gxgnIKk\nEqZ1BExEDgLgVhRU9MyO3pUFOgKWSp97bkVZfNVirHwhzmbSyG5aM6l44cTctiedvRGTNTK96674\nz2lFP6542yZF27TJCF/r1xsNWZP9PNHHMsOnOQ27d2/kwoN4P78mFRwBIzKu3tL9AeAVAHUpHnMP\ngN0Ado8fP16ICsnrly4JduyQbefO6S6lIOxq2CXuh93iesgl+BbE9ZBL3A+7ZVfDLuueJBQSWbbM\nWCq/bJlxe/5843ZtrUgw2Ptxmzdb9/x9EQoZtYRCxu3Nm436li4V2bTJ+Hr0zzN/fuSxsT9P9LHM\n4yxbZvz8mzcb/y2wnz8QCgl27JBvf/CB7lKILAdgt6SRfZTkeFhaKfUygJFx7npQRJ4NP+YVAP8g\naa4Bq6urk927uVyMCsfOlhbM3bsXL19zDW4ZNEh3OQWhzdeW2VZCmYrXxT4UMloxbNvWs1O97g24\nU0lUXygEfP3rwCOPGAvwUz0+069rVPbKK1gzfjwemjRJdylEllJK7RGRupSPy3UASwcDGBW7ly5c\nwG1vv41dtbW4ceBA3eWUhiIKG9Sba+dO3Dt6NP5lioVrAokKQLoBjHtBElnAG17L4ijSNWBFqUg3\noiaDw2aDtwAGAIh00Xq2UErdqZQ6CeB6ANuUUi/orIcoW77wicTJAEaUFodS8HMRPpUw3VdBbgGw\nRWcNRFbwhwOYnVNeRGlx2Gzdb1yIShHfrhNZwHwnzwBGlB67Ut1vXIhKEQMYkQUC4RNJOQMYUVrK\nler+uyEqRQxgRBZgACPKDAMYlToGMCILMIARZYYBjEodAxiRBcwd7coYwIjSUqYUggxgVMIYwIgs\nYJ5IGMCI0mMDEGIAoxLGAEZkAfM0wvhFlB6bUmAXMCplDGBEFjDfyfMPiig9CpE3LkSliOcLIgt0\nj4BxCpIoLQpAIexFTKQLAxiRhRi/iNLDETAqdQxgRBbiCYUofXzDQqWMAYzIAuaJhFMqROnhXwqV\nOgYwIgt0BzCtVRAVjxC4ZpJKGwMYkQXMEwkDGFF6RIQnICpp/P0nskBZ+L/s7E2UnhCMXmBEpYoB\njMgC5omEjSWJ0hMU6X7jQlSKGMCILGBuQcQRMKL0BEU4AkYljQGMyALl4RNJgAGMKC1BRP5uiEoR\nAxiRBRjAiDITEGEAo5LGAEZkAXv4ROJnACNKiz8U6v67ISpFDGBEFugOYCEuwydKh0+EAYxKGgMY\nkQU4AkaUGb8IHDaegqh08befyALO8InEyxEworT4QiE4OAJGJYwBjMgC5jt5H0fAiNLiDYW637gQ\nlSL+9hNZwBl+J9/FETCilEQEXhEGMCpp/O0nskAFpyCJ0maOFDOAUSnjbz+RBcwA1skARpSSOVJc\nyQBGJYy//UQWqCwzdrXjFCRRagxgRAxgRJao5AgYUdo6gkEADGBU2vjbT2SBqvCJxDyxEFFi5hsV\nc+SYqBRpDWBKqe8rpd5TSr2tlNqilBqosx6ibFWFTyTtDGBEKZl/J1UcAaMSpvu3/yUAM0RkJoD3\nAXxdcz1EWXHYbChXCh2cgiRKyQxgLo6AUQnTGsBE5EURCYRv/hHAWJ31EPWFy2bjCBhRGtrDb1QY\nwKiU6R4Bi/bXAH6b6E6l1D1Kqd1Kqd3Nzc15LIsoPdVlZWhjACNKyXyjUs0ARiWsPNdPoJR6GcDI\nOHc9KCLPhh/zIIAAgKcSHUdEngTwJADU1dVxvxcqOAxgROnxhP9O3AxgVMJyHsBE5OPJ7ldK/RWA\nTwG4RYQb6VHxcpeXd59YiCgxT8BYecIARqUs5wEsGaXUPACrAMwVkQ6dtRD1lbusDK2BQOoHEpU4\nD6cgibSvAfshADeAl5RSe5VS/6a5HqKs1ZSVoZUjYEQptQaDqLDZYGcbCiphWkfARGSKzucnslJN\neTlHwIjS0BoIYABHv6jE8e0HkUUGlJdzBIwoDZcCAQwo1/r+n0g7BjAiiwwoK8OlQAC8loQouUvB\nIAMYlTwGMCKLDCwvRwjglZBEKVz0+zGQAYxKHAMYkUXME0oL14ERJdUSCDCAUcljACOyyCC7HQBw\nkQGMKKmLgQAGMYBRiWMAI7LI4PAJ5YLfr7kSosIlIgxgRGAAI7LM4PAI2AWOgBEl1B4Mwi/S/fdC\nVKoYwIgswhEwotTOh9+gDGEAoxLHAEZkEfOEco4BjCih8+G/jyGcgqQSxwBGZJGqsjJU2mwMYERJ\nmAFsKEfAqMQxgBFZaKjd3n2CIaLems0RMAYwKnEMYEQWGma3d59giKg38+9jGAMYlTgGMCILDXc4\nGMCIkmj2+WADeBUklTwGMCILDbPbcdbn010GUcFq9vsx1G6HTSndpRBpxQBGZKHhdjvO+v3ckJso\ngTM+H0Y4HLrLINKOAYzIQiMcDnSGQmjjhtxEcZ31+zGc049EDGBEVjLf2Z/mNCRRXKc5AkYEgAGM\nyFIjwyeWMwxgRL2ICE77fN1/J0SljAGMyELmiaWJAYyoF08wiM5QiAGMCAxgRJYaxQBGlJD5dzGK\nAYyIAYzISkPsdpQrxQBGFEeT1wsAGOV0aq6ESD8GMCIL2ZTCKIcDjeETDRFFNIbfmIzmCBgRAxiR\n1cY4nTjFAEbUi/l3MYYjYEQMYERWG+Nw4BSnIIl6Oen1orqsDDXl5bpLIdKOAYzIYmOdTpzkCBhR\nL6e8Xozl6BcRAAYwIsuNdTrRFgziUiCguxSignKSAYyoGwMYkcXGVVQAAE50dWmuhKiwnPB6MY4B\njAgAAxiR5cwTzAlOQxJ184dCaPL5GMCIwhjAiCxmnmCOM4ARdTvl9UIAjA+PEBOVOgYwIouNdjpR\nrhQaOAVJ1K0h/IZkPEfAiABoDmBKqe8opd5WSu1VSr2olBqtsx4iK5QphbFOJ44zgBF1M9+QXMYR\nMCIA+kfAvi8iM0WkFsBvAPyT5nqILHGZ04ljDGBE3cy/B46AERm0BjARaY266QIgumohstKEigoG\nMKIoDV1dGOlwoKKsTHcpRAVBeztipdRDAP4CwCUAf5bkcfcAuAcAxo8fn5/iiLI0oaICjT4fvKEQ\nnDbdA81E+n3Q1YWJnH4k6pbzM4NS6mWl1P44HwsBQEQeFJFxAJ4CcF+i44jIkyJSJyJ1w4YNy3XZ\nRH0ysbISAnAhPlEYA/HQFioAAAl1SURBVBhRTzkfARORj6f50KcAbAfwzRyWQ5QXk8MnmqOdnbi8\nqkpzNUR6+UMhnOjqwqQRI3SXQlQwdF8FOTXq5kIA7+mqhchKkyorAQBHOQJGhIauLgQReWNCRPrX\ngD2qlJoGIASgAcDfaa6HyBKjHA5U2myo7+zUXQqRdkfCb0TMNyZEpDmAicjdOp+fKFeUUphUUYEj\nDGBE3W9EpjCAEXXj5VlEOTKlshKHGcCIUN/ZiSqbDaMcDt2lEBUMBjCiHJlaVYWjnZ0ICtvbUWk7\n3NGBKZWVUErpLoWoYDCAEeXI1MpKeEVwggvxqcQd7uzEVE4/EvXAAEaUI5eHTzichqRS5g+FcLSr\nC1PZjoWoBwYwohwx+38d6ujQXAmRPse6uhAQwTSOgBH1wABGlCOjHA64y8pwiCNgVMLeC78BYUNi\nop4YwIhyRCmFaVVV3ScgolJkjgBfwQBG1AMDGFEOXVFVhYPt7brLINLmYEcHhtvtGGy36y6FqKAw\ngBHl0JVVVTjl88ETCOguhUiLgx0dHP0iioMBjCiHpodPPAc5DUklSERwsKMD010u3aUQFRwGMKIc\nMk8873IakkrQaZ8PLYFA9xsRIopgACPKoUkVFXAohQMcAaMSdCD8xoMjYES9MYAR5VC5zYYrqqq6\nT0REpcR843EVR8CIemEAI8qxGS4X9jOAUQna396OIeXlGMFNuIl6YQAjyrGrXS6c8HpxiVdCUol5\np60NV1dXcxNuojgYwIhy7OrqagDgKBiVlJAI9re342qu/yKKiwGMKMfME9C+tjbNlRDlzwddXWgP\nhTCTAYwoLgYwohwb53RiUHk53mYAoxJivuG4JjwCTEQ9MYAR5ZhSCjNdLuxlAKMSsq+tDTYAV3EE\njCguBjCiPLimuhrvtLcjKKK7FKK82NfWhqmVlagqK9NdClFBYgAjyoPa6mp0hEKo7+zUXQpRXvyp\nrQ3Xut26yyAqWAxgRHlwbXgdzFsej+ZKiHLvgt+P414varn+iyghBjCiPJjucsGhFP7EdWBUAsw3\nGrMYwIgSYgAjygOHzYarXS7s4QgYlYA94TcaszgFSZQQAxhRntS53XirrQ3ChfjUz73l8WBCRQWG\n2O26SyEqWAxgRHky2+1GSyCAI1yIT/3cbo8Hszn9SJQUAxhRntSFp2N2cxqS+rELfj+OdnV1/74T\nUXwMYER5MsPlglMpBjDq18zf7w/V1GiuhKiwMYAR5YndZsO1bjdeZwCjfuyN1lYogCNgRCkwgBHl\n0XVuN97yeBAIhXSXQpQTr3s8mFZVhQHl5bpLISpoBRHAlFIPKKVEKTVUdy1EuXRdTQ06QiHsb2/X\nXQqR5UQEr7e24jqOfhGlpD2AKaXGAbgNwHHdtRDl2nXhdTF/bG3VXAmR9T7o6kKz39/9e05EiWkP\nYADWAVgFgM2RqN+bWFGBYXY7DnZ06C6FyHLvtrdDAfgIAxhRSlon6ZVSCwGcEpF9SqlUj70HwD3h\nm16l1P5c11dkhgI4p7uIAlOwr8kT4Q9NCvZ10YivSW9ZvyazLC6kwPB3pTe+Jj1dls6DVK67ciul\nXgYwMs5dDwL4PwBuE5FLSqljAOpEJOX/RKXUbhGps7bS4sbXpDe+JvHxdemNr0lvfE3i4+vSG1+T\n7OR8BExEPh7v60qpqwFMBGCOfo0F8JZS6sMicjrXdRERERHpom0KUkTeATDcvJ3JCBgRERFRMSuE\nRfjZeFJ3AQWIr0lvfE3i4+vSG1+T3viaxMfXpTe+JlnI+RowIiIiIuqpWEfAiIiIiIoWAxgRERFR\nnhV9AOM2RhFKqe8opd5WSu1VSr2olBqtuybdlFLfV0q9F35dtiilBuquSTel1GeUUgeUUiGlVElf\nOq6UmqeUOqSUqldKrdFdTyFQSv2HUuosey1GKKXGKaV2KKXeDf/tLNNdk25KqQql1BtKqX3h1+Sf\ndddUbIo6gHEbo16+LyIzRaQWwG8A/JPuggrASwBmiMhMAO8D+LrmegrBfgB3AdipuxCdlFJlAP4V\nwCcBTAfwOaXUdL1VFYT/BDBPdxEFJgDgARGZDuAjAL7K3xV4AdwsItcAqAUwTyn1Ec01FZWiDmDg\nNkY9iEj0BoMu8HWBiLwoIoHwzT/C6DdX0kTkoIgc0l1HAfgwgHoROSoiPgC/ArBQc03aichOABd0\n11FIRKRJRN4Kf+4BcBDAGL1V6SWGtvBNe/ij5M85mSjaABa9jZHuWgqJUuohpdQJAF8AR8Bi/TWA\n3+ouggrGGAAnom6fRImfVCk1pdQEANcCeF1vJfoppcqUUnsBnAXwkoiU/GuSCa17QaaSzjZG+a1I\nv2SviYg8KyIPAnhQKfV1APcB+GZeC9Qg1WsSfsyDMKYRnspnbbqk85oQUWaUUtUANgFYHjPjUJJE\nJAigNry2dotSaoaIcO1gmgo6gHEbo94SvSZxPAVgO0oggKV6TZRSfwXgUwBukRJpfJfB70kpOwVg\nXNTtseGvEfWilLLDCF9Pichm3fUUEhFpUUrtgLF2kAEsTUU5BSki74jIcBGZICITYEwdzOrv4SsV\npdTUqJsLAbynq5ZCoZSaB2Od4AIR6dBdDxWUNwFMVUpNVEo5APw5gK2aa6ICpIx3+j8FcFBE1uqu\npxAopYaZV5UrpSoB3AqeczJSlAGMEnpUKbVfKfU2jOnZkr9UGsAPAbgBvBRuz/FvugvSTSl1p1Lq\nJIDrAWxTSr2guyYdwhdn3AfgBRiLqn8tIgf0VqWfUuqXAP4AYJpS6qRSaonumgrADQC+BODm8L8j\ne5VSt+suSrNRAHaEzzdvwlgD9hvNNRUVbkVERERElGccASMiIiLKMwYwIiIiojxjACMiIiLKMwYw\nIiIiojxjACMiIiLKMwYwIiIiojxjACMiIiLKMwYwIiopSqkdSqlbw59/Vyn1A901EVHpKei9IImI\ncuCbAL6tlBoO4FoACzTXQ0QliJ3wiajkKKVeBVAN4GMi4lFKTQLwIIABIrJIb3VEVAo4BUlEJUUp\ndTWMfex8IuIBABE5KiLc85CI8oYBjIhKhlJqFICnACwE0KaUmqe5JCIqUQxgRFQSlFJVADYDeEBE\nDgL4Doz1YEREecc1YERU8pRSQwA8BOBWABtE5BHNJRFRP8cARkRERJRnnIIkIiIiyjMGMCIiIqI8\nYwAjIiIiyjMGMCIiIqI8YwAjIiIiyjMGMCIiIqI8YwAjIiIiyjMGMCIiIqI8+/8BEkRb1wHTpAUA\nAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(Xbn, Ybn, xlabel=r'$x_1$', ylabel=r'$x_2$')\n", + "plot_decision_boundary_bayes(fig, X_mean, X_std, xmin=-4.0, xmax=4.0, ymin=-4.0, ymax=4.0)" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = [[ -0.31582268]\n", + " [ 0.43496774]\n", + " [ -0.21840373]\n", + " [ -7.88802319]\n", + " [ 22.73897346]\n", + " [ -4.43682364]]\n" + ] + } + ], + "source": [ + "# Uruchomienie metody gradientu prostego dla regresji logistycznej\n", + "theta_start = np.matrix(np.zeros(Xbnp.shape[1])).reshape(Xbnp.shape[1], 1)\n", + "theta, errors = GD(h, J, dJ, theta_start, Xbnp, Ybn, \n", + " alpha=0.05, eps=10**-7, maxSteps=100000)\n", + "print(r'theta = {}'.format(theta))" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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JhgkGMKLhKN6sVayrrgJOPz26ZJisJis2JMWGMSBaS6Z7+WXt2CKq5VG9KjY9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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(Xbnp, Ybn, xlabel=r'$x_1$', ylabel=r'$x_2$')\n", + "plot_decision_boundary(fig, theta, Xbnp, xmin=-4.0, xmax=4.0)" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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YkqQwFT6qlex9H3xQ/Pfpp8WPaO2FTUta/moBFEDZrWWJTX+mULJh6sPTH2LR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\nAzcNmC6FmqgewHo4A0YOZjSAqepjqlq2vnwKwDqT9RBdiB6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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(Xbn, Ybn, xlabel=r'$x_1$', ylabel=r'$x_2$')\n", + "plot_decision_boundary_bayes(fig, X_mean, X_std, xmin=-4.0, xmax=4.0, ymin=-4.0, ymax=4.0)\n", + "plot_decision_boundary(fig, theta, Xbnp, xmin=-4.0, xmax=4.0)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Naiwny klasyfikator Bayesa nie działa, jeżeli dane nie różnią się średnią i odchyleniem standardowym" + ] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15rc1" + }, 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Naiwny klasyfikator bayesowski, drzewa decyzyjne\n", + "### Część 2" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 3.2. Drzewa decyzyjne" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Drzewa decyzyjne – przykład" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przydatne importy\n", + "\n", + "import ipywidgets as widgets\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas\n", + "\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "

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DayOutlookHumidityWindPlay
01SunnyHighWeakNo
12SunnyHighStrongNo
23OvercastHighWeakYes
34RainHighWeakYes
45RainNormalWeakYes
56RainNormalStrongNo
67OvercastNormalStrongYes
78SunnyHighWeakNo
89SunnyNormalWeakYes
910RainNormalWeakYes
1011SunnyNormalStrongYes
1112OvercastHighStrongYes
1213OvercastNormalWeakYes
1314RainHighStrongNo
\n", + "
" + ], + "text/plain": [ + " Day Outlook Humidity Wind Play\n", + "0 1 Sunny High Weak No\n", + "1 2 Sunny High Strong No\n", + "2 3 Overcast High Weak Yes\n", + "3 4 Rain High Weak Yes\n", + "4 5 Rain Normal Weak Yes\n", + "5 6 Rain Normal Strong No\n", + "6 7 Overcast Normal Strong Yes\n", + "7 8 Sunny High Weak No\n", + "8 9 Sunny Normal Weak Yes\n", + "9 10 Rain Normal Weak Yes\n", + "10 11 Sunny Normal Strong Yes\n", + "11 12 Overcast High Strong Yes\n", + "12 13 Overcast Normal Weak Yes\n", + "13 14 Rain High Strong No" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "alldata = pandas.read_csv('tennis.tsv', sep='\\t')\n", + "alldata" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "{'Humidity': {'High', 'Normal'},\n", + " 'Outlook': {'Overcast', 'Rain', 'Sunny'},\n", + " 'Wind': {'Strong', 'Weak'}}" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Dane jako lista słowników\n", + "data = alldata.T.to_dict().values()\n", + "features = ['Outlook', 'Humidity', 'Wind']\n", + "\n", + "# Możliwe wartości w poszczególnych kolumnach\n", + "values = {feature: set(row[feature] for row in data)\n", + " for feature in features}\n", + "values" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Czy John zagra w tenisa, jeżeli będzie padać, przy wysokiej wilgotności i silnym wietrze?\n", + "* Algorytm drzew decyzyjnych spróbuje _zrozumieć_ „taktykę” Johna.\n", + "* Wykorzystamy metodę „dziel i zwyciężaj”." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Podziel dane\n", + "def split(features, data):\n", + " values = {feature: list(set(row[feature]\n", + " for row in data))\n", + " for feature in features}\n", + " if not features:\n", + " return data\n", + " return {val: split(features[1:],\n", + " [row for row in data\n", + " if row[features[0]] == val])\n", + " for val in values[features[0]]}" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\tOutlook\tHumid\tWind\tPlay\n", + "Day 3:\tOvercast\tHigh\tWeak\tYes\n", + "Day 7:\tOvercast\tNormal\tStrong\tYes\n", + "Day 12:\tOvercast\tHigh\tStrong\tYes\n", + "Day 13:\tOvercast\tNormal\tWeak\tYes\n", + "\n", + "\tOutlook\tHumid\tWind\tPlay\n", + "Day 1:\tSunny\tHigh\tWeak\tNo\n", + "Day 2:\tSunny\tHigh\tStrong\tNo\n", + "Day 8:\tSunny\tHigh\tWeak\tNo\n", + "Day 9:\tSunny\tNormal\tWeak\tYes\n", + "Day 11:\tSunny\tNormal\tStrong\tYes\n", + "\n", + "\tOutlook\tHumid\tWind\tPlay\n", + "Day 4:\tRain\tHigh\tWeak\tYes\n", + "Day 5:\tRain\tNormal\tWeak\tYes\n", + "Day 6:\tRain\tNormal\tStrong\tNo\n", + "Day 10:\tRain\tNormal\tWeak\tYes\n", + "Day 14:\tRain\tHigh\tStrong\tNo\n" + ] + } + ], + "source": [ + "split_data = split(['Outlook'], data)\n", + "\n", + "for outlook in values['Outlook']:\n", + " print('\\n\\tOutlook\\tHumid\\tWind\\tPlay')\n", + " for row in split_data[outlook]:\n", + " print('Day {Day}:\\t{Outlook}\\t{Humidity}\\t{Wind}\\t{Play}'\n", + " .format(**row))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Obserwacja: John lubi grać, gdy jest pochmurnie.\n", + "\n", + "W pozostałych przypadkach podzielmy dane ponownie:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\tOutlook\tHumid\tWind\tPlay\n", + "Day 1:\tSunny\tHigh\tWeak\tNo\n", + "Day 2:\tSunny\tHigh\tStrong\tNo\n", + "Day 8:\tSunny\tHigh\tWeak\tNo\n", + "\n", + "\tOutlook\tHumid\tWind\tPlay\n", + "Day 9:\tSunny\tNormal\tWeak\tYes\n", + "Day 11:\tSunny\tNormal\tStrong\tYes\n" + ] + } + ], + "source": [ + "split_data_sunny = split(['Outlook', 'Humidity'], data)\n", + "\n", + "for humidity in values['Humidity']:\n", + " print('\\n\\tOutlook\\tHumid\\tWind\\tPlay')\n", + " for row in split_data_sunny['Sunny'][humidity]:\n", + " print('Day {Day}:\\t{Outlook}\\t{Humidity}\\t{Wind}\\t{Play}'\n", + " .format(**row))" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "\tOutlook\tHumid\tWind\tPlay\n", + "Day 6:\tRain\tNormal\tStrong\tNo\n", + "Day 14:\tRain\tHigh\tStrong\tNo\n", + "\n", + "\tOutlook\tHumid\tWind\tPlay\n", + "Day 4:\tRain\tHigh\tWeak\tYes\n", + "Day 5:\tRain\tNormal\tWeak\tYes\n", + "Day 10:\tRain\tNormal\tWeak\tYes\n" + ] + } + ], + "source": [ + "split_data_rain = split(['Outlook', 'Wind'], data)\n", + "\n", + "for wind in values['Wind']:\n", + " print('\\n\\tOutlook\\tHumid\\tWind\\tPlay')\n", + " for row in split_data_rain['Rain'][wind]:\n", + " print('Day {Day}:\\t{Outlook}\\t{Humidity}\\t{Wind}\\t{Play}'\n", + " .format(**row))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Outlook=\n", + " * Overcast\n", + " * → Playing\n", + " * Sunny\n", + " * Humidity=\n", + " * High\n", + " * → Not playing\n", + " * Normal\n", + " * → Playing\n", + " * Rain\n", + " * Wind=\n", + " * Weak\n", + " * → Playing\n", + " * Strong\n", + " * → Not playing" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* (9/5)\n", + " * Outlook=Overcast (4/0)\n", + " * YES\n", + " * Outlook=Sunny (2/3)\n", + " * Humidity=High (0/3)\n", + " * NO\n", + " * Humidity=Normal (2/0)\n", + " * YES\n", + " * Outlook=Rain (3/2)\n", + " * Wind=Weak (3/0)\n", + " * YES\n", + " * Wind=Strong (0/2)\n", + " * NO" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Algorytm ID3\n", + "\n", + "* podziel(węzeł, zbiór przykładów):\n", + " 1. A ← najlepszy atrybut do podziału zbioru przykładów\n", + " 1. Dla każdej wartości atrybutu A, utwórz nowy węzeł potomny\n", + " 1. Podziel zbiór przykładów na podzbiory według węzłów potomnych\n", + " 1. Dla każdego węzła potomnego i podzbioru:\n", + " * jeżeli podzbiór jest jednolity: zakończ\n", + " * w przeciwnym przypadku: podziel(węzeł potomny, podzbiór)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Jak wybrać „najlepszy atrybut”?\n", + "* powinien zawierać jednolity podzbiór\n", + "* albo przynajmniej „w miarę jednolity”\n", + "\n", + "Skąd wziąć miarę „jednolitości” podzbioru?\n", + "* miara powinna być symetryczna (4/0 vs. 0/4)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Entropia\n", + "\n", + "$$ H(S) = - p_{(+)} \\log p_{(+)} - p_{(-)} \\log p_{(-)} $$\n", + "\n", + "* $S$ – podzbiór przykładów\n", + "* $p_{(+)}$, $p_{(-)}$ – procent pozytywnych/negatywnych przykładów w $S$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Entropię można traktować jako „liczbę bitów” potrzebną do sprawdzenia, czy losowo wybrany $x \\in S$ jest pozytywnym, czy negatywnym przykładem." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Entropia – przykład\n", + "\n", + "* (3 TAK / 3 NIE):\n", + "$$ H(S) = -\\frac{3}{6} \\log\\frac{3}{6} - \\frac{3}{6} \\log\\frac{3}{6} = 1 \\mbox{ bit} $$\n", + "* (4 TAK / 0 NIE):\n", + "$$ H(S) = -\\frac{4}{4} \\log\\frac{4}{4} - \\frac{0}{4} \\log\\frac{0}{4} = 0 \\mbox{ bitów} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### _Information gain_\n", + "\n", + "_Information gain_ – różnica między entropią przed podziałem a entropią po podziale (podczas podziału entropia zmienia się):\n", + "\n", + "$$ \\mathop{\\rm Gain}(S,A) = H(S) - \\sum_{V \\in \\mathop{\\rm Values(A)}} \\frac{|S_V|}{|S|} H(S_V) $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### _Information gain_ – przykład\n", + "\n", + "$$ \\mathop{\\rm Gain}(S, Wind) = H(S) - \\frac{8}{14} H(S_{Wind={\\rm Weak}}) - \\frac{6}{14} H(S_{Wind={\\rm Strong}}) = \\\\\n", + "= 0.94 - \\frac{8}{14} \\cdot 0.81 - \\frac{6}{14} \\cdot 1.0 = 0.049 $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* _Information gain_ jest całkiem sensowną heurystyką wskazującą, który atrybut jest najlepszy do dokonania podziału.\n", + "* **Ale**: _information gain_ przeszacowuje użyteczność atrybutów, które mają dużo różnych wartości.\n", + "* **Przykład**: gdybyśmy wybrali jako atrybut _datę_, otrzymalibyśmy bardzo duży _information gain_, ponieważ każdy podzbiór byłby jednolity, a nie byłoby to ani trochę użyteczne!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### _Information gain ratio_\n", + "\n", + "$$ \\mathop{\\rm GainRatio}(S, A) = \\frac{ \\mathop{\\rm Gain}(S, A) }{ -\\sum_{V \\in \\mathop{\\rm Values}(A)} \\frac{|S_V|}{|S|} \\log\\frac{|S_V|}{|S|} } $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* _Information gain ratio_ może być lepszym wyborem heurystyki wskazującej najużyteczniejszy atrybut, jeżeli atrybuty mają wiele różnych wartości." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Drzewa decyzyjne a formuły logiczne\n", + "\n", + "Drzewo decyzyjne można pzekształcić na formułę logiczną w postaci normalnej (DNF):\n", + "\n", + "$$ Play={\\rm True} \\Leftrightarrow \\left( Outlook={\\rm Overcast} \\vee \\\\\n", + "( Outlook={\\rm Rain} \\wedge Wind={\\rm Weak} ) \\vee \\\\\n", + "( Outlook={\\rm Sunny} \\wedge Humidity={\\rm Normal} ) \\right) $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Klasyfikacja wieloklasowa przy użyciu drzew decyzyjnych\n", + "\n", + "Algorytm przebiega analogicznie, zmienia się jedynie wzór na entropię:\n", + "\n", + "$$ H(S) = -\\sum_{y \\in Y} p_{(y)} \\log p_{(y)} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Skuteczność algorytmu ID3\n", + "\n", + "* Przyjmujemy, że wśród danych uczących nie ma duplikatów (tj. przykładów, które mają jednakowe cechy $x$, a mimo to należą do różnych klas $y$).\n", + "* Wówczas algorytm drzew decyzyjnych zawsze znajdzie rozwiązanie, ponieważ w ostateczności będziemy mieli węzły 1-elementowe na liściach drzewa." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Nadmierne dopasowanie drzew decyzyjnych\n", + "\n", + "* Zauważmy, że w miarę postępowania algorytmu dokładność przewidywań drzewa (_accuracy_) liczona na zbiorze uczącym dąży do 100% (i w ostateczności osiąga 100%, nawet kosztem jednoelementowych liści).\n", + "* Takie rozwiązanie niekoniecznie jest optymalne. Dokładność na zbiorze testowym może być dużo niższa, a to oznacza nadmierne dopasowanie." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Jak zapobiec nadmiernemu dopasowaniu?\n", + "\n", + "Aby zapobiegać nadmiernemu dopasowaniu drzew decyzyjnych, należy je przycinać (_pruning_)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Można tego dokonywać na kilka sposobów:\n", + "* Można zatrzymywać procedurę podziału w pewnym momencie (np. kiedy podzbiory staja się zbyt małe).\n", + "* Można najpierw wykonać algorytm ID3 w całości, a następnie przyciąć drzewo, np. kierując się wynikami uzyskanymi na zbiorze walidacyjnym.\n", + "* Algorytm _sub-tree replacement pruning_ (algorytm zachłanny)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### _Sub-tree replacement pruning_\n", + "\n", + "1. Dla każdego węzła:\n", + " 1. Udaj, że usuwasz węzeł wraz z całym zaczepionym w nim poddrzewem.\n", + " 1. Dokonaj ewaluacji na zbiorze walidacyjnym.\n", + "1. Usuń węzeł, którego usunięcie daje największą poprawę wyniku.\n", + "1. Powtarzaj, dopóki usuwanie węzłów poprawia wynik." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Zalety drzew decyzyjnych\n", + "\n", + "* Zasadę działania drzew decyzyjnych łatwo zrozumieć człowiekowi.\n", + "* Atrybuty, które nie wpływają na wynik, mają _gain_ równy 0, zatem są od razu pomijane przez algorytm.\n", + "* Po zbudowaniu, drzewo decyzyjne jest bardzo szybkim klasyfikatorem (złożoność $O(d)$, gdzie $d$ jest głębokościa dzewa)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Wady drzew decyzyjnych\n", + "\n", + "* ID3 jest algorytmem zachłannym – może nie wskazać najlepszego drzewa.\n", + "* Nie da się otrzymać granic klas (_decision boundaries_), które nie są równoległe do osi wykresu." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 3.3. Lasy losowe" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Algorytm lasów losowych – idea\n", + "\n", + "* Algorytm lasów losowych jest rozwinięciem algorytmu ID3.\n", + "* Jest to bardzo wydajny algorytm klasyfikacji.\n", + "* Zamiast jednego, będziemy budować $k$ drzew." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Algorytm lasów losowych – budowa lasu\n", + "\n", + "1. Weź losowy podzbiór $S_r$ zbioru uczącego.\n", + "1. Zbuduj pełne (tj. bez przycinania) drzewo decyzyjne dla $S_r$, używając algorytmu ID3 z następującymi modyfikacjami:\n", + " * podczas podziału używaj losowego $d$-elementowego podzbioru atrybutów,\n", + " * obliczaj _gain_ względem $S_r$.\n", + "1. Powyższą procedurę powtórz $k$-krotnie, otrzymując $k$ drzew ($T_1, T_2, \\ldots, T_k$)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Algorytm lasów losowych – predykcja\n", + "\n", + "1. Sklasyfikuj $x$ według każdego z drzew $T_1, T_2, \\ldots, T_k$ z osobna.\n", + "1. Użyj głosowania większościowego: przypisz klasę przewidzianą przez najwięcej drzew." + ] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15rc1" + }, + "livereveal": { + "start_slideshow_at": "selected", + "theme": "amu" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/w3/zumz3b.pdf b/w3/zumz3b.pdf new file mode 100644 index 0000000000000000000000000000000000000000..0789320903c689216b71147de5f49eab21a0fa25 GIT binary patch literal 52469 zcma&NQ_L_xlWzOkwr$(CZQHhO+cv(}wr$(Ct^H4OE@o$TPUfal7nQ#2Rjcx(NfkuI zXc_5Pp-7MKZ{DF883-5%?2W9TczEc=ENxs&o#@4E3|&k`OpWbLOzCAz?aW;)2pE|d 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index 0000000..2ee7967 --- /dev/null +++ b/w4/iris.csv @@ -0,0 +1,151 @@ +łod.dł.,łod.sz.,pł.dł.,pł.sz.,Gatunek +5.2,3.4,1.4,0.2,Iris-setosa +5.1,3.7,1.5,0.4,Iris-setosa +6.7,3.1,5.6,2.4,Iris-virginica +6.5,3.2,5.1,2.0,Iris-virginica +4.9,2.5,4.5,1.7,Iris-virginica +6.0,2.7,5.1,1.6,Iris-versicolor +5.7,2.6,3.5,1.0,Iris-versicolor +5.0,2.0,3.5,1.0,Iris-versicolor +5.2,3.5,1.5,0.2,Iris-setosa +4.8,3.0,1.4,0.1,Iris-setosa +6.7,3.3,5.7,2.5,Iris-virginica +6.1,3.0,4.9,1.8,Iris-virginica +4.8,3.4,1.9,0.2,Iris-setosa +5.8,2.8,5.1,2.4,Iris-virginica +4.4,2.9,1.4,0.2,Iris-setosa +7.2,3.0,5.8,1.6,Iris-virginica +4.4,3.2,1.3,0.2,Iris-setosa +5.0,3.5,1.3,0.3,Iris-setosa +5.4,3.9,1.3,0.4,Iris-setosa +7.7,2.8,6.7,2.0,Iris-virginica +5.0,3.6,1.4,0.2,Iris-setosa +6.2,2.8,4.8,1.8,Iris-virginica +6.0,2.2,5.0,1.5,Iris-virginica +7.4,2.8,6.1,1.9,Iris-virginica +5.0,3.2,1.2,0.2,Iris-setosa +6.7,3.1,4.4,1.4,Iris-versicolor +6.7,3.1,4.7,1.5,Iris-versicolor +5.6,2.7,4.2,1.3,Iris-versicolor 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Algorytm KNN, uczenie nienadzorowane\n", + "### Część 1" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 4.1. Algorytm $k$ najbliższych sąsiadów" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### KNN – intuicja" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Do której kategorii powinien należeć punkt oznaczony gwiazdką?" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przydatne importy\n", + "\n", + "import ipywidgets as widgets\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas\n", + "\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wczytanie danych (gatunki kosaćców)\n", + "\n", + "data_iris_setosa = (\n", + " pandas.read_csv('iris.csv', usecols=['pł.dł.', 'pł.sz.', 'Gatunek'])\n", + " .apply(lambda x: [x[0], x[1], 1 if x[2] == 'Iris-setosa' else 0], axis=1))\n", + "data_iris_setosa.columns = ['dł. płatka', 'szer. płatka', 'Iris setosa?']\n", + "\n", + "m, n_plus_1 = data_iris_setosa.values.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data_iris_setosa.values[:, 0:n].reshape(m, n)\n", + "\n", + "X = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n", + "Y = np.matrix(data_iris_setosa.values[:, 2]).reshape(m, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wykres danych (wersja macierzowa)\n", + "def plot_data_for_classification(X, Y, xlabel, ylabel): \n", + " fig = plt.figure(figsize=(16*.6, 9*.6))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + " X = X.tolist()\n", + " Y = Y.tolist()\n", + " X1n = [x[1] for x, y in zip(X, Y) if y[0] == 0]\n", + " X1p = [x[1] for x, y in zip(X, Y) if y[0] == 1]\n", + " X2n = [x[2] for x, y in zip(X, Y) if y[0] == 0]\n", + " X2p = [x[2] for x, y in zip(X, Y) if y[0] == 1]\n", + " ax.scatter(X1n, X2n, c='r', marker='x', s=50, label='Dane')\n", + " ax.scatter(X1p, X2p, c='g', marker='o', s=50, label='Dane')\n", + " \n", + " ax.set_xlabel(xlabel)\n", + " ax.set_ylabel(ylabel)\n", + " ax.margins(.05, .05)\n", + " return fig" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def plot_new_example(fig, x, y):\n", + " ax = fig.axes[0]\n", + " ax.scatter([x], [y], c='k', marker='*', s=100, label='?')" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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dOUcIAEBrIvlqUuseXKeyl+vuK3tZ6x5YFzgiAAAgkXw1rW0vbXv1jtdIu/fu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\nyd1/I0lmdkvl5zmKEqced38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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n", + "plot_new_example(fig, 2.8, 0.9)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Wydaje się sensownym przyjąć, że punkt oznaczony gwiazdką powinien być czerwony, ponieważ sąsiednie punkty są czerwone. Najbliższe czerwone punkty są położone bliżej niż najbliższe zielone." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Algorytm oparty na tej intuicji nazywamy algorytmem **$k$ najbliższych sąsiadów** (_$k$ nearest neighbors_, KNN)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Idea (KNN dla $k = 1$):\n", + " 1. Dla nowego przykładu $x'$ znajdź najbliższy przykład $x$ ze zbioru uczącego.\n", + " 1. Jego klasa $y$ to szukana klasa $y'$." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "from scipy.spatial import Voronoi, voronoi_plot_2d\n", + "\n", + "def plot_voronoi(fig, points):\n", + " ax = fig.axes[0]\n", + " vor = Voronoi(points)\n", + " ax.scatter(vor.vertices[:, 0], vor.vertices[:, 1], s=1)\n", + " \n", + " for simplex in vor.ridge_vertices:\n", + " simplex = np.asarray(simplex)\n", + " if np.all(simplex >= 0):\n", + " ax.plot(vor.vertices[simplex, 0], vor.vertices[simplex, 1],\n", + " color='orange', linewidth=1)\n", + " \n", + " xmin, ymin = points.min(axis=0).tolist()[0]\n", + " xmax, ymax = points.max(axis=0).tolist()[0]\n", + " pad = 0.1\n", + " ax.set_xlim(xmin - pad, xmax + pad)\n", + " ax.set_ylim(ymin - pad, ymax + pad)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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C4CzB9jOAsy4yDGvT7iEgYiSw/0ntkwHazwDSfuBsTJ0QzteNiJAa8m4ihgP5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\nz5hqZB9bUrtGZOWAy3E4AjGT/PGIH9sIkXvIWJv1UXhWiB/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T59GF0d3tvUnSVKlLufdN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m5UuoaEN4bIppB3xGpPFHrp/ggc/B/Yiq32xDRU8BXI7PoH2Arh/L+7dt3ZFXLFK36AOX5ZTUgo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\nAAAAAElFTkSuQmCC\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(X, Y, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n", + "plot_new_example(fig, 2.8, 0.9)\n", + "plot_voronoi(fig, X[:, 1:])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Podział płaszczyzny jak na powyższym wykresie nazywamy **diagramem Woronoja** (_Voronoi diagram_)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Taki algorytm wyznacza dość efektowne granice klas, zwłaszcza jak na tak prosty algorytm. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Niestety jest bardzo podatny na obserwacje odstające:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "X_outliers = np.vstack((X, np.matrix([[1.0, 3.9, 1.7]])))\n", + "Y_outliers = np.vstack((Y, np.matrix([[1]])))" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "data": { + "image/png": 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1arbh7v0QHaTfiebKZIoDHvHy/ep2qlmKrn9RKQ3CwYX1KiKyQXeI/0A9sCMZkbJGi9td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\narS9f5n1o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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(X_outliers, Y_outliers, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n", + "plot_new_example(fig, 2.8, 0.9)\n", + "plot_voronoi(fig, X_outliers[:, 1:])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Pojedyncza obserwacja odstająca dramatycznie zmienia granice klas." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Aby temu zaradzić, użyjemy więcej niż jednego najbliższego sąsiada ($k > 1$)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Algorytm $k$ najbliższych sąsiadów dla problemu klasyfikacji\n", + "\n", + "1. Dany jest zbiór uczący zawierajacy przykłady $(x_i, y_i)$, gdzie: $x_i$ – zestaw cech, $y_i$ – klasa.\n", + "1. Dany jest przykład testowy $x'$, dla którego chcemy określić klasę.\n", + "1. Oblicz odległość $d(x', x_i)$ dla każdego przykładu $x_i$ ze zbioru uczącego.\n", + "1. Wybierz $k$ przykładów $x_{i_1}, \\ldots, x_{i_k}$, dla których wyliczona odległość jest najmniejsza.\n", + "1. Jako wynik $y'$ zwróć tę spośrod klas $y_{i_1}, \\ldots, y_{i_k}$, która występuje najczęściej." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Algorytm $k$ najbliższych sąsiadów dla problemu klasyfikacji – przykład" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [], + "source": [ + "# Odległość euklidesowa\n", + "def euclidean_distance(x1, x2):\n", + " return np.linalg.norm(x1 - x2)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Algorytm k najbliższych sąsiadów\n", + "def knn(X, Y, x_new, k, distance=euclidean_distance):\n", + " data = np.concatenate((X, Y), axis=1)\n", + " nearest = sorted(\n", + " data, key=lambda xy:distance(xy[0, :-1], x_new))[:k]\n", + " y_nearest = [xy[0, -1] for xy in nearest]\n", + " return max(y_nearest, key=lambda y:y_nearest.count(y))" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wykres klas dla KNN\n", + "def plot_knn(fig, X, Y, k, distance=euclidean_distance):\n", + " ax = fig.axes[0]\n", + " x1min, x2min = X.min(axis=0).tolist()[0]\n", + " x1max, x2max = X.max(axis=0).tolist()[0]\n", + " pad1 = (x1max - x1min) / 10\n", + " pad2 = (x2max - x2min) / 10\n", + " step1 = (x1max - x1min) / 50\n", + " step2 = (x2max - x2min) / 50\n", + " x1grid, x2grid = np.meshgrid(\n", + " np.arange(x1min - pad1, x1max + pad1, step1),\n", + " np.arange(x2min - pad2, x2max + pad2, step2))\n", + " z = np.matrix([[knn(X, Y, [x1, x2], k, distance) \n", + " for x1, x2 in zip(x1row, x2row)] \n", + " for x1row, x2row in zip(x1grid, x2grid)])\n", + " plt.contour(x1grid, x2grid, z, levels=[0.5]);" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przygotowanie interaktywnego wykresu\n", + "\n", + "slider_k = widgets.IntSlider(min=1, max=10, step=1, value=1, description=r'$k$', width=300)\n", + "\n", + "def interactive_knn_1(k):\n", + " fig = plot_data_for_classification(X_outliers, Y_outliers, xlabel=u'dł. płatka', ylabel=u'szer. płatka')\n", + " plot_voronoi(fig, X_outliers[:, 1:])\n", + " plot_knn(fig, X_outliers[:, 1:], Y_outliers, k)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "652f2d8ba643479298bc4e252b59474f", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

Failed to display Jupyter Widget of type interactive.

\n", + "

\n", + " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", + " that the widgets JavaScript is still loading. If this message persists, it\n", + " likely means that the widgets JavaScript library is either not installed or\n", + " not enabled. See the Jupyter\n", + " Widgets Documentation for setup instructions.\n", + "

\n", + "

\n", + " If you're reading this message in another notebook frontend (for example, a static\n", + " rendering on GitHub or NBViewer),\n", + " it may mean that your frontend doesn't currently support widgets.\n", + "

\n" + ], + "text/plain": [ + "interactive(children=(IntSlider(value=1, description=u'$k$', max=10, min=1), Button(description=u'Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "widgets.interact_manual(interactive_knn_1, k=slider_k)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wczytanie danych (inny przykład)\n", + "\n", + "alldata = pandas.read_csv('classification.tsv', sep='\\t')\n", + "data = np.matrix(alldata)\n", + "\n", + "m, n_plus_1 = data.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data[:, 1:].reshape(m, n)\n", + "\n", + "X2 = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n", + "Y2 = np.matrix(data[:, 0]).reshape(m, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(X2, Y2, xlabel=r'$x_1$', ylabel=r'$x_2$')" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przygotowanie interaktywnego wykresu\n", + "\n", + "slider_k = widgets.IntSlider(min=1, max=10, step=1, value=1, description=r'$k$', width=300)\n", + "\n", + "def interactive_knn_2(k):\n", + " fig = plot_data_for_classification(X2, Y2, xlabel=r'$x_1$', ylabel=r'$x_2$')\n", + " plot_voronoi(fig, X2[:, 1:])\n", + " plot_knn(fig, X2[:, 1:], Y2, k)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "a10b0ca5c82349b596c12857fda3cd55", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

Failed to display Jupyter Widget of type interactive.

\n", + "

\n", + " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", + " that the widgets JavaScript is still loading. If this message persists, it\n", + " likely means that the widgets JavaScript library is either not installed or\n", + " not enabled. See the Jupyter\n", + " Widgets Documentation for setup instructions.\n", + "

\n", + "

\n", + " If you're reading this message in another notebook frontend (for example, a static\n", + " rendering on GitHub or NBViewer),\n", + " it may mean that your frontend doesn't currently support widgets.\n", + "

\n" + ], + "text/plain": [ + "interactive(children=(IntSlider(value=1, description=u'$k$', max=10, min=1), Button(description=u'Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "widgets.interact_manual(interactive_knn_2, k=slider_k)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Algorytm $k$ najbliższych sąsiadów dla problemu regresji\n", + "\n", + "1. Dany jest zbiór uczący zawierajacy przykłady $(x_i, y_i)$, gdzie: $x_i$ – zestaw cech, $y_i$ – liczba rzeczywista.\n", + "1. Dany jest przykład testowy $x'$, dla którego chcemy określić klasę.\n", + "1. Oblicz odległość $d(x', x_i)$ dla każdego przykładu $x_i$ ze zbioru uczącego.\n", + "1. Wybierz $k$ przykładów $x_{i_1}, \\ldots, x_{i_k}$, dla których wyliczona odległość jest najmniejsza.\n", + "1. Jako wynik $y'$ zwróć średnią liczb $y_{i_1}, \\ldots, y_{i_k}$:\n", + " $$ y' = \\frac{1}{k} \\sum_{j=1}^{k} y_{i_j} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Wybór $k$\n", + "\n", + "* Wartość $k$ ma duży wpływ na wynik działania algorytmu KNN:\n", + " * Jeżeli $k$ jest zbyt duże, wszystkie nowe przykłady są klasyfikowane jako klasa większościowa.\n", + " * Jeżeli $k$ jest zbyt małe, granice klas są niestabilne, a algorytm jest bardzo podatny na obserwacje odstające.\n", + "* Aby dobrać optymalną wartość $k$, najlepiej użyć zbioru walidacyjnego." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Miary podobieństwa" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Odległość euklidesowa\n", + "$$ d(x, x') = \\sqrt{ \\sum_{i=1}^n \\left( x_i - x'_i \\right) ^2 } $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Dobry wybór w przypadku numerycznych cech.\n", + "* Symetryczna, traktuje wszystkie wymiary jednakowo.\n", + "* Wrażliwa na duże wahania jednej cechy." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Odległość Hamminga\n", + "$$ d(x, x') = \\sum_{i=1}^n \\mathbf{1}_{x_i \\neq x'_i} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Dobry wybór w przypadku cech zero-jedynkowych.\n", + "* Liczba cech, którymi różnią się dane przykłady." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Odległość Minkowskiego ($p$-norma)\n", + "$$ d(x, x') = \\sqrt[p]{ \\sum_{i=1}^n \\left| x_i - x'_i \\right| ^p } $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Dla $p = 2$ jest to odległość euklidesowa.\n", + "* Dla $p = 1$ jest to odległość taksówkowa.\n", + "* Jeżeli $p \\to \\infty$, to $p$-norma zbliża się do logicznej alternatywy.\n", + "* Jeżeli $p \\to 0$, to $p$-norma zbliża się do logicznej koniunkcji." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### KNN – praktyczne porady" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Co zrobić z remisami?\n", + " * losowanie\n", + " * prawdopodobieństwo _a priori_\n", + " * 1NN" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* KNN źle radzi sobie z brakującymi wartościami cech (nie można wówczas sensownie wyznaczyć odległości)." + ] 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Algorytm KNN, uczenie nienadzorowane\n", + "### Część 2" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 4.2. Uczenie nienadzorowane – Algorytm $k$ średnich" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przydatne importy\n", + "\n", + "import ipywidgets as widgets\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import pandas\n", + "import random\n", + "import seaborn\n", + "\n", + "%matplotlib inline" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wczytanie danych (gatunki kosaćców)\n", + "\n", + "data_iris = pandas.read_csv('iris.csv', header=0, usecols=['łod.dł.', 'łod.sz.', 'pł.dł.', 'pł.sz.'])\n", + "data_iris.columns=['x1', 'x2', 'x3', 'x4']\n", + "\n", + "X = data_iris.values\n", + "Xs = data_iris.values[:, 2:4]" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wykres danych\n", + "def plot_unlabeled_data(X, col1=0, col2=1, x1label=r'$x_1$', x2label=r'$x_2$'): \n", + " fig = plt.figure(figsize=(16*.7, 9*.7))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + " X1 = X[:, col1].tolist()\n", + " X2 = X[:, col2].tolist()\n", + " ax.scatter(X1, X2, c='k', marker='o', s=50, label='Dane')\n", + " ax.set_xlabel(x1label)\n", + " ax.set_ylabel(x2label)\n", + " ax.margins(.05, .05)\n", + " return fig" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przygotowanie interaktywnego wykresu\n", + "\n", + "dropdown_arg1 = widgets.Dropdown(options=[0, 1, 2, 3], value=2, description='arg1')\n", + "dropdown_arg2 = widgets.Dropdown(options=[0, 1, 2, 3], value=3, description='arg2')\n", + "\n", + "def interactive_unlabeled_data(arg1, arg2):\n", + " fig = plot_unlabeled_data(\n", + " X, col1=arg1, col2=arg2, x1label='$x_{}$'.format(arg1), x2label='$x_{}$'.format(arg2))" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "4196201adbb34356bf7a5f511a8206f9", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

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\n", + " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", + " that the widgets JavaScript is still loading. If this message persists, it\n", + " likely means that the widgets JavaScript library is either not installed or\n", + " not enabled. See the Jupyter\n", + " Widgets Documentation for setup instructions.\n", + "

\n", + "

\n", + " If you're reading this message in another notebook frontend (for example, a static\n", + " rendering on GitHub or NBViewer),\n", + " it may mean that your frontend doesn't currently support widgets.\n", + "

\n" + ], + "text/plain": [ + "interactive(children=(Dropdown(description=u'arg1', index=2, options=(0, 1, 2, 3), value=2), Dropdown(description=u'arg2', index=3, options=(0, 1, 2, 3), value=3), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "widgets.interact(interactive_unlabeled_data, arg1=dropdown_arg1, arg2=dropdown_arg2)" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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LYdP5Jy6EhTHdTro90/VJVNIwnQfcVKbRLQtLgIrG5dRYi5oHlSET/ubfsz7n5D9+tgAj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ryi3dFvn0uwedAQsXBjc49RL0phI4j8xTaNzSOaVu2u+owXX39pr+VYZDW+eF0iNiyo1ccS2/Ex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\nuSfVxL0AAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "seaborn.pairplot(data_iris, vars=data_iris.columns, size=1.5, aspect=1.75)" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Odległość euklidesowa\n", + "def euclidean_distance(x1, x2):\n", + " return np.linalg.norm(x1 - x2)" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Algorytm k średnich\n", + "def k_means(X, k, distance=euclidean_distance):\n", + " history = []\n", + " Y = []\n", + " \n", + " # Wylosuj centroid dla każdej klasy\n", + " centroids = [[random.uniform(X.min(axis=0)[f], X.max(axis=0)[f])\n", + " for f in range(X.shape[1])]\n", + " for c in range(k)]\n", + "\n", + " # Powtarzaj, dopóki klasy się zmieniają\n", + " while True:\n", + " distances = [[distance(centroids[c], x) for c in range(k)] for x in X]\n", + " Y_new = [d.index(min(d)) for d in distances]\n", + " if Y_new == Y:\n", + " break\n", + " Y = Y_new\n", + " XY = np.asarray(np.concatenate((X, np.matrix(Y).T), axis=1))\n", + " Xc = [XY[XY[:, 2] == c][:, :-1] for c in range(k)]\n", + " centroids = [[Xc[c].mean(axis=0)[f] for f in range(X.shape[1])]\n", + " for c in range(k)]\n", + " history.append((centroids, Y))\n", + "\n", + " result = history[-1][1]\n", + " return result, history" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wykres danych - klastrowanie\n", + "def plot_clusters(X, Y, k, centroids=None):\n", + " color = ['r', 'g', 'b', 'c', 'm', 'y', 'k']\n", + " fig = plt.figure(figsize=(16*.7, 9*.7))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + "\n", + " X1 = X[:, 0].tolist()\n", + " X2 = X[:, 1].tolist()\n", + " X1 = [[x for x, y in zip(X1, Y) if y == c] for c in range(k)]\n", + " X2 = [[x for x, y in zip(X2, Y) if y == c] for c in range(k)]\n", + "\n", + " for c in range(k):\n", + " ax.scatter(X1[c], X2[c], c=color[c], marker='o', s=25, label='Dane')\n", + " if centroids:\n", + " ax.scatter([centroids[c][0]], [centroids[c][1]], c=color[c], marker='+', s=500, label='Centroid')\n", + "\n", + " ax.set_xlabel(r'$x_1$')\n", + " ax.set_ylabel(r'$x_2$')\n", + " ax.margins(.05, .05)\n", + " return fig" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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P7r++e0OS7wFAB0IvACBdtmyR7rgj/BlXMbwHIDIsbwAAAED0CL0AAACIHqEXAAAA0SP0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\n/3QUdeHStU+3deB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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Ys, history = k_means(Xs, 2)\n", + "fig = plot_clusters(Xs, Ys, 2, centroids=history[-1][0])" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przygotowanie interaktywnego wykresu\n", + "\n", + "slider_k = widgets.IntSlider(min=1, max=7, step=1, value=2, description=r'$k$', width=300)\n", + "\n", + "def interactive_kmeans_k(steps, history, k):\n", + " if steps >= len(history) or steps == 10:\n", + " steps = len(history) - 1\n", + " fig = plot_clusters(Xs, history[steps][1], k, centroids=history[steps][0])\n", + " \n", + "def interactive_kmeans(k):\n", + " slider_steps = widgets.IntSlider(min=1, max=10, step=1, value=1, description=r'steps', width=300)\n", + " _, history = k_means(Xs, k)\n", + " widgets.interact(interactive_kmeans_k, steps=slider_steps,\n", + " history=widgets.fixed(history), k=widgets.fixed(k))" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "41f26926f3cc4de6acf9239e228e775a", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

Failed to display Jupyter Widget of type interactive.

\n", + "

\n", + " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", + " that the widgets JavaScript is still loading. If this message persists, it\n", + " likely means that the widgets JavaScript library is either not installed or\n", + " not enabled. See the Jupyter\n", + " Widgets Documentation for setup instructions.\n", + "

\n", + "

\n", + " If you're reading this message in another notebook frontend (for example, a static\n", + " rendering on GitHub or NBViewer),\n", + " it may mean that your frontend doesn't currently support widgets.\n", + "

\n" + ], + "text/plain": [ + "interactive(children=(IntSlider(value=2, description=u'$k$', max=7, min=1), Button(description=u'Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "widgets.interact_manual(interactive_kmeans, k=slider_k)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Algorytm $k$ średnich – dane wejściowe\n", + "\n", + "* $k$ – liczba klastrów\n", + "* zbiór uczący $X = \\{ x^{(1)}, x^{(2)}, \\ldots, x^{(m)} \\}$, $x^{(i)} \\in \\mathbb{R}^n$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Na wejściu nie ma zbioru $Y$, ponieważ jest to uczenie nienadzorowane!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Algorytm $k$ średnich – pseudokod\n", + "\n", + "1. Zainicjalizuj losowo $k$ centroidów (środków ciężkości klastrów): $\\mu_1, \\ldots, \\mu_k$.\n", + "1. Powtarzaj dopóki przyporządkowania klastrów się zmieniają:\n", + " 1. Dla $i = 1$ do $m$:\n", + " za $y^{(i)}$ przyjmij klasę najbliższego centroidu.\n", + " 1. Dla $c = 1$ do $k$:\n", + " za $\\mu_c$ przyjmij średnią wszystkich punktów $x^{(i)}$ takich, że $y^{(i)} = c$." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Algorytm k średnich\n", + "def k_means(X, k, distance=euclidean_distance):\n", + " Y = []\n", + " centroids = [[random.uniform(X.min(axis=0)[f],X.max(axis=0)[f])\n", + " for f in range(X.shape[1])]\n", + " for c in range(k)] # Wylosuj centroidy\n", + " while True:\n", + " distances = [[distance(centroids[c], x) for c in range(k)]\n", + " for x in X] # Oblicz odległości\n", + " Y_new = [d.index(min(d)) for d in distances]\n", + " if Y_new == Y:\n", + " break # Jeśli nic się nie zmienia, przerwij\n", + " Y = Y_new\n", + " XY = np.asarray(np.concatenate((X,np.matrix(Y).T),axis=1))\n", + " Xc = [XY[XY[:, 2] == c][:, :-1] for c in range(k)]\n", + " centroids = [[Xc[c].mean(axis=0)[f]\n", + " for f in range(X.shape[1])]\n", + " for c in range(k)] # Przesuń centroidy\n", + " return Y" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Liczba klastrów jest określona z góry i wynosi $k$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Jeżeli w którymś kroku algorytmu jedna z klas nie zostanie przyporządkowana żadnemu z przykładów, pomija się ją – w ten sposób wynikiem działania algorytmu może być mniej niż $k$ klastrów." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Funkcja kosztu dla problemu klastrowania\n", + "\n", + "$$ J \\left( y^{(i)}, \\ldots, y^{(m)}, \\mu_{1}, \\ldots, \\mu_{k} \\right) = \\frac{1}{m} \\sum_{i=1}^{m} || x^{(i)} - \\mu_{y^{(i)}} || ^2 $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Zauważmy, że z każdym krokiem algorytmu $k$ średnich koszt się zmniejsza (lub ewentualnie pozostaje taki sam)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Wielokrotna inicjalizacja\n", + "\n", + "* Algorytm $k$ średnich zawsze znajdzie lokalne minimum funkcji kosztu $J$, ale nie zawsze będzie to globalne minimum." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Aby temu zaradzić, można uruchomić algorytm $k$ średnich wiele razy, za każdym razem z innym losowym położeniem centroidów (tzw. **wielokrotna losowa inicjalizacja** – _multiple random initialization_).\n", + "* Za każdym razem obliczamy koszt $J$. Wybieramy ten wynik, który ma najniższy koszt." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Wybór liczby klastrów $k$\n", + "\n", + "* Najlepiej wybrać $k$ ręcznie w zależności od kształtu danych i celu, który chcemy osiągnąć." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 4.3. Metryki" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def powerme(x1,x2,n):\n", + " X = []\n", + " for m in range(n+1):\n", + " for i in range(m+1):\n", + " X.append(np.multiply(np.power(x1,i),np.power(x2,(m-i))))\n", + " return np.hstack(X)" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wykres danych\n", + "def plot_data_for_classification(X, Y, xlabel=None, ylabel=None, Y_predicted=[], highlight=None):\n", + " fig = plt.figure(figsize=(16*.6, 9*.6))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + " X = X.tolist()\n", + " Y = Y.tolist()\n", + " X1n = [x[1] for x, y in zip(X, Y) if y[0] == 0]\n", + " X1p = [x[1] for x, y in zip(X, Y) if y[0] == 1]\n", + " X2n = [x[2] for x, y in zip(X, Y) if y[0] == 0]\n", + " X2p = [x[2] for x, y in zip(X, Y) if y[0] == 1]\n", + " \n", + " if Y_predicted != []:\n", + " Y_predicted = Y_predicted.tolist()\n", + " X1tn = [x[1] for x, y, yp in zip(X, Y, Y_predicted) if y[0] == 0 and yp[0] == 0]\n", + " X1fn = [x[1] for x, y, yp in zip(X, Y, Y_predicted) if y[0] == 1 and yp[0] == 0]\n", + " X1tp = [x[1] for x, y, yp in zip(X, Y, Y_predicted) if y[0] == 1 and yp[0] == 1]\n", + " X1fp = [x[1] for x, y, yp in zip(X, Y, Y_predicted) if y[0] == 0 and yp[0] == 1]\n", + " X2tn = [x[2] for x, y, yp in zip(X, Y, Y_predicted) if y[0] == 0 and yp[0] == 0]\n", + " X2fn = [x[2] for x, y, yp in zip(X, Y, Y_predicted) if y[0] == 1 and yp[0] == 0]\n", + " X2tp = [x[2] for x, y, yp in zip(X, Y, Y_predicted) if y[0] == 1 and yp[0] == 1]\n", + " X2fp = [x[2] for x, y, yp in zip(X, Y, Y_predicted) if y[0] == 0 and yp[0] == 1]\n", + " \n", + " if Y_predicted != []:\n", + " if highlight == 'tn':\n", + " ax.scatter(X1tn, X2tn, c='r', marker='x', s=50, label='Dane')\n", + " ax.scatter(X1fn, X2fn, c='k', marker='o', s=50, label='Dane')\n", + " ax.scatter(X1tp, X2tp, c='k', marker='o', s=50, label='Dane')\n", + " ax.scatter(X1fp, X2fp, c='k', marker='x', s=50, label='Dane')\n", + " elif highlight == 'fn':\n", + " ax.scatter(X1tn, X2tn, c='k', marker='x', s=50, label='Dane')\n", + " ax.scatter(X1fn, X2fn, c='r', marker='o', s=50, label='Dane')\n", + " ax.scatter(X1tp, X2tp, c='k', marker='o', s=50, label='Dane')\n", + " ax.scatter(X1fp, X2fp, c='k', marker='x', s=50, label='Dane')\n", + " elif highlight == 'tp':\n", + " ax.scatter(X1tn, X2tn, c='k', marker='x', s=50, label='Dane')\n", + " ax.scatter(X1fn, X2fn, c='k', marker='o', s=50, label='Dane')\n", + " ax.scatter(X1tp, X2tp, c='g', marker='o', s=50, label='Dane')\n", + " ax.scatter(X1fp, X2fp, c='k', marker='x', s=50, label='Dane')\n", + " elif highlight == 'fp':\n", + " ax.scatter(X1tn, X2tn, c='k', marker='x', s=50, label='Dane')\n", + " ax.scatter(X1fn, X2fn, c='k', marker='o', s=50, label='Dane')\n", + " ax.scatter(X1tp, X2tp, c='k', marker='o', s=50, label='Dane')\n", + " ax.scatter(X1fp, X2fp, c='g', marker='x', s=50, label='Dane')\n", + " else:\n", + " ax.scatter(X1tn, X2tn, c='r', marker='x', s=50, label='Dane')\n", + " ax.scatter(X1fn, X2fn, c='r', marker='o', s=50, label='Dane')\n", + " ax.scatter(X1tp, X2tp, c='g', marker='o', s=50, label='Dane')\n", + " ax.scatter(X1fp, X2fp, c='g', marker='x', s=50, label='Dane')\n", + "\n", + " else:\n", + " ax.scatter(X1n, X2n, c='r', marker='x', s=50, label='Dane')\n", + " ax.scatter(X1p, X2p, c='g', marker='o', s=50, label='Dane')\n", + " \n", + " if xlabel:\n", + " ax.set_xlabel(xlabel)\n", + " if ylabel:\n", + " ax.set_ylabel(ylabel)\n", + " \n", + " ax.margins(.05, .05)\n", + " return fig" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wczytanie danych\n", + "import pandas\n", + "import numpy as np\n", + "\n", + "alldata = pandas.read_csv('data.tsv', sep='\\t')\n", + "data = np.matrix(alldata)\n", + "\n", + "m, n_plus_1 = data.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data[:, 1:]\n", + "\n", + "X2 = powerme(data[:, 1], data[:, 2], n)\n", + "Y2 = np.matrix(data[:, 0]).reshape(m, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig = plot_data_for_classification(X2, Y2, xlabel=r'$x_1$', ylabel=r'$x_2$')" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def safeSigmoid(x, eps=0):\n", + " y = 1.0/(1.0 + np.exp(-x))\n", + " if eps > 0:\n", + " y[y < eps] = eps\n", + " y[y > 1 - eps] = 1 - eps\n", + " return y\n", + "\n", + "def h(theta, X, eps=0.0):\n", + " return safeSigmoid(X*theta, eps)\n", + "\n", + "def J(h,theta,X,y, lamb=0):\n", + " m = len(y)\n", + " f = h(theta, X, eps=10**-7)\n", + " j = -np.sum(np.multiply(y, np.log(f)) + \n", + " np.multiply(1 - y, np.log(1 - f)), axis=0)/m\n", + " if lamb > 0:\n", + " j += lamb/(2*m) * np.sum(np.power(theta[1:],2))\n", + " return j\n", + "\n", + "def dJ(h,theta,X,y,lamb=0):\n", + " g = 1.0/y.shape[0]*(X.T*(h(theta,X)-y))\n", + " if lamb > 0:\n", + " g[1:] += lamb/float(y.shape[0]) * theta[1:] \n", + " return g\n", + "\n", + "def classifyBi(theta, X):\n", + " prob = h(theta, X)\n", + " return prob" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Metoda gradientu prostego dla regresji logistycznej\n", + "def GD(h, fJ, fdJ, theta, X, y, alpha=0.01, eps=10**-3, maxSteps=10000):\n", + " errorCurr = fJ(h, theta, X, y)\n", + " errors = [[errorCurr, theta]]\n", + " while True:\n", + " # oblicz nowe theta\n", + " theta = theta - alpha * fdJ(h, theta, X, y)\n", + " # raportuj poziom błędu\n", + " errorCurr, errorPrev = fJ(h, theta, X, y), errorCurr\n", + " # kryteria stopu\n", + " if abs(errorPrev - errorCurr) <= eps:\n", + " break\n", + " if len(errors) > maxSteps:\n", + " break\n", + " errors.append([errorCurr, theta]) \n", + " return theta, errors" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "theta = [[ 1.37136167]\n", + " [ 0.90128948]\n", + " [ 0.54708112]\n", + " [-5.9929264 ]\n", + " [ 2.64435168]\n", + " [-4.27978238]]\n" + ] + } + ], + "source": [ + "# Uruchomienie metody gradientu prostego dla regresji logistycznej\n", + "theta_start = np.matrix(np.zeros(X2.shape[1])).reshape(X2.shape[1],1)\n", + "theta, errors = GD(h, J, dJ, theta_start, X2, Y2, \n", + " alpha=0.1, eps=10**-7, maxSteps=10000)\n", + "print('theta = {}'.format(theta))" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Wykres granicy klas\n", + "def plot_decision_boundary(fig, theta, X):\n", + " ax = fig.axes[0]\n", + " xx, yy = np.meshgrid(np.arange(-1.0, 1.0, 0.02),\n", + " np.arange(-1.0, 1.0, 0.02))\n", + " l = len(xx.ravel())\n", + " C = powerme(xx.reshape(l, 1), yy.reshape(l, 1), n)\n", + " z = classifyBi(theta, C).reshape(int(np.sqrt(l)), int(np.sqrt(l)))\n", + "\n", + " plt.contour(xx, yy, z, levels=[0.5], lw=3);" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "matrix([[0],\n", + " [1],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [0],\n", + " [1],\n", + " [1],\n", + " [1],\n", + " [0]])" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "Y_predicted = (classifyBi(theta, X2) > 0.5).astype(int)\n", + "Y_predicted[:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "# Przygotowanie interaktywnego wykresu\n", + "\n", + "dropdown_highlight = widgets.Dropdown(options=['all', 'tp', 'fp', 'tn', 'fn'], value='all', description='highlight')\n", + "\n", + "def interactive_classification(highlight):\n", + " fig = plot_data_for_classification(X2, Y2, xlabel=r'$x_1$', ylabel=r'$x_2$',\n", + " Y_predicted=Y_predicted, highlight=highlight)\n", + " plot_decision_boundary(fig, theta, X2)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "d66ed3534beb4ceb998f948bbb7f348c", + "version_major": 2, + "version_minor": 0 + }, + "text/html": [ + "

Failed to display Jupyter Widget of type interactive.

\n", + "

\n", + " If you're reading this message in Jupyter Notebook or JupyterLab, it may mean\n", + " that the widgets JavaScript is still loading. If this message persists, it\n", + " likely means that the widgets JavaScript library is either not installed or\n", + " not enabled. See the Jupyter\n", + " Widgets Documentation for setup instructions.\n", + "

\n", + "

\n", + " If you're reading this message in another notebook frontend (for example, a static\n", + " rendering on GitHub or NBViewer),\n", + " it may mean that your frontend doesn't currently support widgets.\n", + "

\n" + ], + "text/plain": [ + "interactive(children=(Dropdown(description=u'highlight', options=('all', 'tp', 'fp', 'tn', 'fn'), value='all'), Output()), _dom_classes=('widget-interact',))" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "widgets.interact(interactive_classification, highlight=dropdown_highlight)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Dokładność (_accuracy_):\n", + "$$ accuracy = \\frac{tp + tn}{tp + fp + tn + fn} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Precyzja (_precision_):\n", + " $$ precision = \\frac{tp}{tp + fp} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Pokrycie (_recall_):\n", + " $$ recall = \\frac{tp}{tp + fn} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "_$F$-measure_:\n", + "$$ F = \\frac{2 \\cdot precision \\cdot recall}{precision + recall} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "_$F_\\beta$-measure_:\n", + "$$ F_\\beta = \\frac{(1 + \\beta) \\cdot precision \\cdot recall}{\\beta^2 * precision + recall} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* $F = F_1$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 4.4. Analiza głównych składowych" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Redukcja liczby wymiarów\n", + "\n", + "Z jakich powodów chcemy redukować liczbę wymiarów?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Chcemy pozbyć się nadmiarowych cech, np. „długość w cm” / „długość w calach”, „długość” i „szerokość” / „powierzchnia”." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Chcemy znaleźć bardziej optymalną kombinację cech." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Chcemy przyspieszyć działanie algorytmów." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Chcemy zwizualizować dane." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Błąd rzutowania\n", + "\n", + "**Błąd rzutowania** – błąd średniokwadratowy pomiędzy danymi oryginalnymi a danymi zrzutowanymi." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Sformułowanie problemu\n", + "\n", + "**Analiza głównych składowych** (_Principal Component Analysis_, PCA):\n", + "\n", + "Zredukować liczbę wymiarów z $n$ do $k$, czyli znaleźć $k$ wektorów $u^{(1)}, u^{(2)}, \\ldots, u^{(k)}$ takich, że rzutowanie danych na podprzeztrzeń rozpiętą na tych wektorach minimalizuje błąd rzutowania." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Analiza głównych składowych to zupełnie inne zagadnienie niż regresja liniowa!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Algorytm PCA\n", + "\n", + "1. Dany jest zbiór składający się z $x^{(1)}, x^{(2)}, \\ldots, x^{(m)} \\in \\mathbb{R}^n$.\n", + "1. Chcemy zredukować liczbę wymiarów z $n$ do $k$ ($k < n$).\n", + "1. W ramach wstępnego przetwarzania dokonujemy skalowania i normalizacji średniej.\n", + "1. Znajdujemy macierz kowariancji:\n", + " $$ \\Sigma = \\frac{1}{m} \\sum_{i=1}^{n} \\left( x^{(i)} \\right) \\left( x^{(i)} \\right)^T $$\n", + "1. Znajdujemy wektory własne macierzy $\\Sigma$ (rozkład SVD):\n", + " $$ (U, S, V) := \\mathop{\\rm SVD}(\\Sigma) $$\n", + "1. Pierwszych $k$ kolumn macierzy $U$ to szukane wektory." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "from sklearn.preprocessing import StandardScaler\n", + "\n", + "# Algorytm PCA - implementacja\n", + "def pca(X, k):\n", + " X_std = StandardScaler().fit_transform(X) # normalizacja\n", + " mean_vec = np.mean(X_std, axis=0)\n", + " cov_mat = np.cov(X_std.T) # macierz kowariancji\n", + " n = cov_mat.shape[0]\n", + " eig_vals, eig_vecs = np.linalg.eig(cov_mat) # wektory własne\n", + " eig_pairs = [(np.abs(eig_vals[i]), eig_vecs[:, i])\n", + " for i in range(len(eig_vals))]\n", + " eig_pairs.sort()\n", + " eig_pairs.reverse()\n", + " matrix_w = np.hstack([eig_pairs[i][1].reshape(n, 1)\n", + " for i in range(k)]) # wybór\n", + " return X_std.dot(matrix_w) # transformacja" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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Sieci neuronowe" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import math\n", + "import matplotlib\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import random" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 5.1. Perceptron" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "scrolled": true, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/jpeg": 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b+tY0obTf4jtZMc/ks6rcFzxlEBCKQ7D2SdGmkQroKgab67Wl3lB17q9fut5a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\ndEJJKaybM7khzO6JJJqw2YzsmGqSSiv/2Q==\n", + "text/html": [ + "\n", + " \n", + " " + ], + "text/plain": [ + "" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from IPython.display import YouTubeVideo\n", + "YouTubeVideo('cNxadbrN_aI', width=800, height=600)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\"Frank" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\"Frank" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "\"perceptron\"/" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Pierwszy perceptron liniowy\n", + "\n", + "* Frank Rosenblatt, 1957\n", + "* aparat fotograficzny podłączony do 400 fotokomórek (rozdzielczość obrazu: 20 x 20)\n", + "* wagi – potencjometry aktualizowane za pomocą silniczków" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Uczenie perceptronu\n", + "\n", + "Cykl uczenia perceptronu Rosenblatta:\n", + "\n", + "1. Sfotografuj planszę z kolejnym obiektem.\n", + "1. Zaobserwuj, która lampka zapaliła się na wyjściu.\n", + "1. Sprawdź, czy to jest właściwa lampka.\n", + "1. Wyślij sygnał „nagrody” lub „kary”." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Funkcja aktywacji\n", + "\n", + "Funkcja bipolarna:\n", + "\n", + "$$ g(z) = \\left\\{ \n", + "\\begin{array}{rl}\n", + "1 & \\textrm{gdy $z > \\theta_0$} \\\\\n", + "-1 & \\textrm{wpp.}\n", + "\\end{array}\n", + "\\right. $$\n", + "\n", + "gdzie $z = \\theta_0x_0 + \\ldots + \\theta_nx_n$,
    \n", + "$\\theta_0$ to próg aktywacji,
    \n", + "$x_0 = 1$. " + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def bipolar_plot():\n", + " matplotlib.rcParams.update({'font.size': 16})\n", + "\n", + " plt.figure(figsize=(8,5))\n", + " x = [-1,-.23,1] \n", + " y = [-1, -1, 1]\n", + " plt.ylim(-1.2,1.2)\n", + " plt.xlim(-1.2,1.2)\n", + " plt.plot([-2,2],[1,1], color='black', ls=\"dashed\")\n", + " plt.plot([-2,2],[-1,-1], color='black', ls=\"dashed\")\n", + " plt.step(x, y, lw=3)\n", + " ax = plt.gca()\n", + " ax.spines['right'].set_color('none')\n", + " ax.spines['top'].set_color('none')\n", + " ax.xaxis.set_ticks_position('bottom')\n", + " ax.spines['bottom'].set_position(('data',0))\n", + " ax.yaxis.set_ticks_position('left')\n", + " ax.spines['left'].set_position(('data',0))\n", + "\n", + " plt.annotate(r'$\\theta_0$',\n", + " xy=(-.23,0), xycoords='data',\n", + " xytext=(-50, +50), textcoords='offset points', fontsize=26,\n", + " arrowprops=dict(arrowstyle=\"->\"))\n", + "\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "bipolar_plot()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Perceptron – schemat\n", + "\n", + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Perceptron – zasada działania\n", + "\n", + "1. Ustal wartości początkowe $\\theta$ (wektor 0 lub liczby losowe blisko 0).\n", + "1. Dla każdego przykładu $(x^{(i)}, y^{(i)})$, dla $i=1,\\ldots,m$\n", + " * Oblicz wartość wyjścia $o^{(i)}$:\n", + " $$o^{(i)} = g(\\theta^{T}x^{(i)}) = g(\\sum_{j=0}^{n} \\theta_jx_j^{(i)})$$\n", + " * Wykonaj aktualizację wag (tzw. _perceptron rule_):\n", + " $$ \\theta := \\theta + \\Delta \\theta $$\n", + " $$ \\Delta \\theta = \\alpha(y^{(i)}-o^{(i)})x^{(i)} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "$$\\theta_j := \\theta_j + \\Delta \\theta_j $$\n", + "\n", + "Jeżeli przykład został sklasyfikowany **poprawnie**:\n", + "\n", + "* $y^{(i)}=1$ oraz $o^{(i)}=1$ : $$\\Delta\\theta_j = \\alpha(1 - 1)x_j^{(i)} = 0$$\n", + "* $y^{(i)}=-1$ oraz $o^{(i)}=-1$ : $$\\Delta\\theta_j = \\alpha(-1 - -1)x_j^{(i)} = 0$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Czyli: jeżeli trafiłeś, to nic nie zmieniaj." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "$$\\theta_j := \\theta_j + \\Delta \\theta_j $$\n", + "\n", + "Jeżeli przykład został sklasyfikowany **niepoprawnie**:\n", + "\n", + "* $y^{(i)}=1$ oraz $o^{(i)}=-1$ : $$\\Delta\\theta_j = \\alpha(1 - -1)x_j^{(i)} = 2 \\alpha x_j^{(i)}$$\n", + "* $y^{(i)}=-1$ oraz $o^{(i)}=1$ : $$\\Delta\\theta_j = \\alpha(-1 - 1)x_j^{(i)} = -2 \\alpha x_j^{(i)}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Czyli: przesuń wagi w odpowiednią stronę." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Perceptron – zalety i wady\n", + "\n", + "Zalety:\n", + "* intuicyjny i prosty\n", + "* łatwy w implementacji\n", + "* jeżeli dane można liniowo oddzielić, algorytm jest zbieżny w skończonym czasie" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Wady:\n", + "* jeżeli danych nie można oddzielić liniowo, algorytm nie jest zbieżny" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def plot_perceptron():\n", + " plt.figure(figsize=(12,3))\n", + "\n", + " plt.subplot(131)\n", + " plt.ylim(-0.2,1.2)\n", + " plt.xlim(-0.2,1.2)\n", + "\n", + " plt.title('AND')\n", + " plt.plot([1,0,0], [0,1,0], 'ro', markersize=10)\n", + " plt.plot([1], [1], 'go', markersize=10)\n", + "\n", + " ax = plt.gca()\n", + " ax.spines['right'].set_color('none')\n", + " ax.spines['top'].set_color('none')\n", + " ax.xaxis.set_ticks_position('none')\n", + " ax.spines['bottom'].set_position(('data',0))\n", + " ax.yaxis.set_ticks_position('none')\n", + " ax.spines['left'].set_position(('data',0))\n", + "\n", + " plt.xticks(np.arange(0, 2, 1.0))\n", + " plt.yticks(np.arange(0, 2, 1.0))\n", + "\n", + "\n", + " plt.subplot(132)\n", + " plt.ylim(-0.2,1.2)\n", + " plt.xlim(-0.2,1.2)\n", + "\n", + " plt.plot([1,0,1], [0,1,1], 'go', markersize=10)\n", + " plt.plot([0], [0], 'ro', markersize=10)\n", + "\n", + " ax = plt.gca()\n", + " ax.spines['right'].set_color('none')\n", + " ax.spines['top'].set_color('none')\n", + " ax.xaxis.set_ticks_position('none')\n", + " ax.spines['bottom'].set_position(('data',0))\n", + " ax.yaxis.set_ticks_position('none')\n", + " ax.spines['left'].set_position(('data',0))\n", + "\n", + " plt.title('OR')\n", + " plt.xticks(np.arange(0, 2, 1.0))\n", + " plt.yticks(np.arange(0, 2, 1.0))\n", + "\n", + "\n", + " plt.subplot(133)\n", + " plt.ylim(-0.2,1.2)\n", + " plt.xlim(-0.2,1.2)\n", + "\n", + " plt.title('XOR')\n", + " plt.plot([1,0], [0,1], 'go', markersize=10)\n", + " plt.plot([0,1], [0,1], 'ro', markersize=10)\n", + "\n", + " ax = plt.gca()\n", + " ax.spines['right'].set_color('none')\n", + " ax.spines['top'].set_color('none')\n", + " ax.xaxis.set_ticks_position('none')\n", + " ax.spines['bottom'].set_position(('data',0))\n", + " ax.yaxis.set_ticks_position('none')\n", + " ax.spines['left'].set_position(('data',0))\n", + "\n", + " plt.xticks(np.arange(0, 2, 1.0))\n", + " plt.yticks(np.arange(0, 2, 1.0))\n", + "\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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AAIBgEWYBAAAQLMIsAAAAgkWYBQAAQLAIswAAAAgWYRYAAADBIswCAAAgWIRZAAAABIsw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\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_perceptron()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Funkcje aktywacji\n", + "\n", + "Zamiast funkcji bipolarnej możemy zastosować funkcję sigmoidalną jako funkcję aktywacji." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def plot_activation_functions():\n", + " plt.figure(figsize=(16,7))\n", + " plt.subplot(121)\n", + " x = [-2,-.23,2] \n", + " y = [-1, -1, 1]\n", + " plt.ylim(-1.2,1.2)\n", + " plt.xlim(-2.2,2.2)\n", + " plt.plot([-2,2],[1,1], color='black', ls=\"dashed\")\n", + " plt.plot([-2,2],[-1,-1], color='black', ls=\"dashed\")\n", + " plt.step(x, y, lw=3)\n", + " ax = plt.gca()\n", + " ax.spines['right'].set_color('none')\n", + " ax.spines['top'].set_color('none')\n", + " ax.xaxis.set_ticks_position('bottom')\n", + " ax.spines['bottom'].set_position(('data',0))\n", + " ax.yaxis.set_ticks_position('left')\n", + " ax.spines['left'].set_position(('data',0))\n", + "\n", + " plt.annotate(r'$\\theta_0$',\n", + " xy=(-.23,0), xycoords='data',\n", + " xytext=(-50, +50), textcoords='offset points', fontsize=26,\n", + " arrowprops=dict(arrowstyle=\"->\"))\n", + "\n", + " plt.subplot(122)\n", + " x2 = np.linspace(-2,2,100)\n", + " y2 = np.tanh(x2+ 0.23)\n", + " plt.ylim(-1.2,1.2)\n", + " plt.xlim(-2.2,2.2)\n", + " plt.plot([-2,2],[1,1], color='black', ls=\"dashed\")\n", + " plt.plot([-2,2],[-1,-1], color='black', ls=\"dashed\")\n", + " plt.plot(x2, y2, lw=3)\n", + " ax = plt.gca()\n", + " ax.spines['right'].set_color('none')\n", + " ax.spines['top'].set_color('none')\n", + " ax.xaxis.set_ticks_position('bottom')\n", + " ax.spines['bottom'].set_position(('data',0))\n", + " ax.yaxis.set_ticks_position('left')\n", + " ax.spines['left'].set_position(('data',0))\n", + "\n", + " plt.annotate(r'$\\theta_0$',\n", + " xy=(-.23,0), xycoords='data',\n", + " xytext=(-50, +50), textcoords='offset points', fontsize=26,\n", + " arrowprops=dict(arrowstyle=\"->\"))\n", + "\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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RpKreuL+F/L340R/2w7sJAAAAcAK74lP00MItOnPxyk11RnUJ1+huDeTG9ZCwM4IkAAAA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\nvLxcubm5TvX8/HwlJyerpKREr776qlN92bJlSkh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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot_activation_functions()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Perceptron a regresja liniowa" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Uczenie regresji liniowej:\n", + "* Model: $$h_{\\theta}(x) = \\sum_{i=0}^n \\theta_ix_i$$\n", + "* Funkcja kosztu (błąd średniokwadratowy): $$J(\\theta) = \\frac{1}{m} \\sum_{i=1}^{m} (h_{\\theta}(x^{(i)}) - y^{(i)})^2$$\n", + "\n", + "* Po obliczeniu $\\nabla J(\\theta)$, zwykły SGD." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Perceptron a dwuklasowa regresja logistyczna" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Uczenie dwuklasowej regresji logistycznej:\n", + "* Model: $$h_{\\theta}(x) = \\sigma(\\sum_{i=0}^n \\theta_ix_i) = P(1|x,\\theta)$$\n", + "* Funkcja kosztu (entropia krzyżowa): $$\\begin{eqnarray} J(\\theta) &=& -\\frac{1}{m} \\sum_{i=1}^{m} [y^{(i)}\\log P(1|x^{(i)},\\theta) \\\\ && + (1-y^{(i)})\\log(1-P(1|x^{(i)},\\theta))]\\end{eqnarray}$$\n", + "\n", + "* Po obliczeniu $\\nabla J(\\theta)$, zwykły SGD." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Perceptron a wieloklasowa regresja logistyczna" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Wieloklasowa regresji logistyczna\n", + "* Model (dla $c$ klasyfikatorów binarnych): \n", + "$$\\begin{eqnarray}\n", + "h_{(\\theta^{(1)},\\dots,\\theta^{(c)})}(x) &=& \\mathrm{softmax}(\\sum_{i=0}^n \\theta_{i}^{(1)}x_i, \\ldots, \\sum_{i=0}^n \\theta_i^{(c)}x_i) \\\\ \n", + "&=& \\left[ P(k|x,\\theta^{(1)},\\dots,\\theta^{(c)}) \\right]_{k=1,\\dots,c} \n", + "\\end{eqnarray}$$\n", + "* Funkcja kosztu (**przymując model regresji binarnej**): $$\\begin{eqnarray} J(\\theta^{(k)}) &=& -\\frac{1}{m} \\sum_{i=1}^{m} [y^{(i)}\\log P(k|x^{(i)},\\theta^{(k)}) \\\\ && + (1-y^{(i)})\\log P(\\neg k|x^{(i)},\\theta^{(k)})]\\end{eqnarray}$$\n", + "\n", + "* Po obliczeniu $\\nabla J(\\theta)$, **c-krotne** uruchomienie SGD, zastosowanie $\\mathrm{softmax}(X)$ do niezależnie uzyskanych klasyfikatorów binarnych." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Przyjmijmy: \n", + "$$ \\Theta = (\\theta^{(1)},\\dots,\\theta^{(c)}) $$\n", + "\n", + "$$h_{\\Theta}(x) = \\left[ P(k|x,\\Theta) \\right]_{k=1,\\dots,c}$$\n", + "\n", + "$$\\delta(x,y) = \\left\\{\\begin{array}{cl} 1 & \\textrm{gdy } x=y \\\\ 0 & \\textrm{wpp.}\\end{array}\\right.$$\n", + "\n", + "* Wieloklasowa funkcja kosztu $J(\\Theta)$ (kategorialna entropia krzyżowa):\n", + "$$ J(\\Theta) = -\\frac{1}{m}\\sum_{i=1}^{m}\\sum_{k=1}^{c} \\delta({y^{(i)},k}) \\log P(k|x^{(i)},\\Theta) $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Gradient $\\nabla J(\\Theta)$:\n", + "$$ \\dfrac{\\partial J(\\Theta)}{\\partial \\Theta_{j,k}} = -\\frac{1}{m}\\sum_{i = 1}^{m} (\\delta({y^{(i)},k}) - P(k|x^{(i)}, \\Theta)) x^{(i)}_j \n", + "$$\n", + "\n", + "* Liczymy wszystkie wagi jednym uruchomieniem SGD" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "## Podsumowanie\n", + "\n", + "* W przypadku jednowarstowej sieci neuronowej wystarczy znać gradient funkcji kosztu.\n", + "* Wtedy liczymy tak samo jak w przypadku regresji liniowej, logistycznej, wieloklasowej logistycznej itp.\n", + " * Wymienione modele to szczególne przypadki jednowarstwowych sieci neuronowych.\n", + "* Regresja liniowa i binarna regresja logistyczna to jeden neuron.\n", + "* Wieloklasowa regresja logistyczna to tyle neuronów ile klas." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Funkcja aktywacji i funkcja kosztu są **dobierane do problemu**." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 5.2. Wielowarstwowe sieci neuronowe\n", + "\n", + "czyli _Artificial Neural Networks_ (ANN) lub _Multi-Layer Perceptrons_ (MLP)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Architektura sieci\n", + "\n", + "* Sieć neuronowa jako graf neuronów. \n", + "* Organizacja sieci przez warstwy.\n", + "* Najczęściej stosowane są sieci jednokierunkowe i gęste." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* $n$-warstwowa sieć neuronowa ma $n+1$ warstw (nie liczymy wejścia).\n", + "* Rozmiary sieci określane poprzez liczbę neuronów lub parametrów." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Sieć neuronowa jednokierunkowa (_feedforward_)\n", + "\n", + "* Mając daną $n$-warstwową sieć neuronową oraz jej parametry $\\Theta^{(1)}, \\ldots, \\Theta^{(L)} $ oraz $\\beta^{(1)}, \\ldots, \\beta^{(L)} $ liczymy:

    \n", + "$$a^{(l)} = g^{(l)}\\left( a^{(l-1)} \\Theta^{(l)} + \\beta^{(l)} \\right). $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Funkcje $g^{(l)}$ to tzw. **funkcje aktywacji**.
    \n", + "Dla $i = 0$ przyjmujemy $a^{(0)} = \\mathrm{x}$ (wektor wierszowy cech) oraz $g^{(0)}(x) = x$ (identyczność)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Parametry $\\Theta$ to wagi na połączeniach miedzy neuronami dwóch warstw.
    \n", + "Rozmiar macierzy $\\Theta^{(l)}$, czyli macierzy wag na połączeniach warstw $a^{(l-1)}$ i $a^{(l)}$, to $\\dim(a^{(l-1)}) \\times \\dim(a^{(l)})$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Parametry $\\beta$ zastępują tutaj dodawanie kolumny z jedynkami do macierzy cech.
    Macierz $\\beta^{(l)}$ ma rozmiar równy liczbie neuronów w odpowiedniej warstwie, czyli $1 \\times \\dim(a^{(l)})$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* **Klasyfikacja**: dla ostatniej warstwy $L$ (o rozmiarze równym liczbie klas) przyjmuje się $g^{(L)}(x) = \\mathop{\\mathrm{softmax}}(x)$.\n", + "* **Regresja**: pojedynczy neuron wyjściowy jak na obrazku. Funkcją aktywacji może wtedy być np. funkcja identycznościowa." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Pozostałe funkcje aktywacji najcześciej mają postać sigmoidy, np. sigmoidalna, tangens hiperboliczny.\n", + "* Mogą mieć też inny kształt, np. ReLU, leaky ReLU, maxout." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 5.3. Metoda propagacji wstecznej – wprowadzenie" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Jak uczyć sievi neuronowe?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* W poznanych do tej pory algorytmach (regresja liniowa, regresja logistyczna) do uczenia używaliśmy funkcji kosztu, jej gradientu oraz algorytmu gradientu prostego (GD/SGD)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Dla sieci neuronowych potrzebowalibyśmy również znaleźć gradnient funkcji kosztu." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Co sprowadza się do bardziej ogólnego problemu:
    jak obliczyć gradient $\\nabla f(x)$ dla danej funkcji $f$ i wektora wejściowego $x$?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Pochodna funkcji\n", + "\n", + "* **Pochodna** mierzy, jak szybko zmienia się wartość funkcji względem zmiany jej argumentów:\n", + "\n", + "$$ \\frac{d f(x)}{d x} = \\lim_{h \\to 0} \\frac{ f(x + h) - f(x) }{ h } $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Pochodna cząstkowa i gradient\n", + "\n", + "* **Pochodna cząstkowa** mierzy, jak szybko zmienia się wartość funkcji względem zmiany jej *pojedynczego argumentu*." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* **Gradient** to wektor pochodnych cząstkowych:\n", + "\n", + "$$ \\nabla f = \\left( \\frac{\\partial f}{\\partial x_1}, \\ldots, \\frac{\\partial f}{\\partial x_n} \\right) $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Gradient – przykłady\n", + "\n", + "$$ f(x_1, x_2) = x_1 + x_2 \\qquad \\to \\qquad \\frac{\\partial f}{\\partial x_1} = 1, \\quad \\frac{\\partial f}{\\partial x_2} = 1, \\quad \\nabla f = (1, 1) $$ " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$ f(x_1, x_2) = x_1 \\cdot x_2 \\qquad \\to \\qquad \\frac{\\partial f}{\\partial x_1} = x_2, \\quad \\frac{\\partial f}{\\partial x_2} = x_1, \\quad \\nabla f = (x_2, x_1) $$ " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$ f(x_1, x_2) = \\max(x_1 + x_2) \\hskip{12em} \\\\\n", + "\\to \\qquad \\frac{\\partial f}{\\partial x_1} = \\mathbb{1}_{x \\geq y}, \\quad \\frac{\\partial f}{\\partial x_2} = \\mathbb{1}_{y \\geq x}, \\quad \\nabla f = (\\mathbb{1}_{x \\geq y}, \\mathbb{1}_{y \\geq x}) $$ " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Własności pochodnych cząstkowych\n", + "\n", + "Jezeli $f(x, y, z) = (x + y) \\, z$ oraz $x + y = q$, to:\n", + "$$f = q z,\n", + "\\quad \\frac{\\partial f}{\\partial q} = z,\n", + "\\quad \\frac{\\partial f}{\\partial z} = q,\n", + "\\quad \\frac{\\partial q}{\\partial x} = 1,\n", + "\\quad \\frac{\\partial q}{\\partial y} = 1 $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Reguła łańcuchowa\n", + "\n", + "$$ \\frac{\\partial f}{\\partial x} = \\frac{\\partial f}{\\partial q} \\, \\frac{\\partial q}{\\partial x},\n", + "\\quad \\frac{\\partial f}{\\partial y} = \\frac{\\partial f}{\\partial q} \\, \\frac{\\partial q}{\\partial y} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Propagacja wsteczna – prosty przykład" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# Dla ustalonego wejścia\n", + "x = -2; y = 5; z = -4" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(3, -12)\n" + ] + } + ], + "source": [ + "# Krok w przód\n", + "q = x + y\n", + "f = q * z\n", + "print(q, f)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-4, -4, 3]\n" + ] + } + ], + "source": [ + "# Propagacja wsteczna dla f = q * z\n", + "dz = q\n", + "dq = z\n", + "# Propagacja wsteczna dla q = x + y\n", + "dx = 1 * dq # z reguły łańcuchowej\n", + "dy = 1 * dq # z reguły łańcuchowej\n", + "print([dx, dy, dz])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Właśnie tak wygląda obliczanie pochodnych metodą propagacji wstecznej!" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Spróbujmy czegoś bardziej skomplikowanego:
    metodą propagacji wstecznej obliczmy pochodną funkcji sigmoidalnej." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Propagacja wsteczna – funkcja sigmoidalna" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Funkcja sigmoidalna:\n", + "\n", + "$$f(\\theta,x) = \\frac{1}{1+e^{-(\\theta_0 x_0 + \\theta_1 x_1 + \\theta_2)}}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.3932238664829637, -0.5898357997244456]\n", + "[-0.19661193324148185, -0.3932238664829637, 0.19661193324148185]\n" + ] + } + ], + "source": [ + "import math\n", + "\n", + "# Losowe wagi i dane\n", + "w = [2,-3,-3]\n", + "x = [-1, -2]\n", + "\n", + "# Krok w przód\n", + "dot = w[0]*x[0] + w[1]*x[1] + w[2]\n", + "f = 1.0 / (1 + math.exp(-dot)) # funkcja sigmoidalna\n", + "\n", + "# Krok w tył\n", + "ddot = (1 - f) * f # pochodna funkcji sigmoidalnej\n", + "dx = [w[0] * ddot, w[1] * ddot]\n", + "dw = [x[0] * ddot, x[1] * ddot, 1.0 * ddot]\n", + "\n", + "print(dx)\n", + "print(dw)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Obliczanie gradientów – podsumowanie\n", + "\n", + "* Gradient $f$ dla $x$ mówi jak zmieni się całe wyrażenie przy zmianie wartości $x$.\n", + "* Gradienty łączymy korzystając z **reguły łańcuchowej**.\n", + "* W kroku wstecz gradienty informują, które części grafu powinny być zwiększone lub zmniejszone (i z jaką siłą), aby zwiększyć wartość na wyjściu.\n", + "* W kontekście implementacji chcemy dzielić funkcję $f$ na części, dla których można łatwo obliczyć gradienty." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 5.4. Uczenie wielowarstwowych sieci neuronowych metodą propagacji wstecznej" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Mając algorytm SGD oraz gradienty wszystkich wag, moglibyśmy trenować każdą sieć." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Niech:\n", + "$$\\Theta = (\\Theta^{(1)},\\Theta^{(2)},\\Theta^{(3)},\\beta^{(1)},\\beta^{(2)},\\beta^{(3)})$$\n", + "\n", + "* Funkcja sieci neuronowej z grafiki:\n", + "\n", + "$$\\small h_\\Theta(x) = \\tanh(\\tanh(\\tanh(x\\Theta^{(1)}+\\beta^{(1)})\\Theta^{(2)} + \\beta^{(2)})\\Theta^{(3)} + \\beta^{(3)})$$\n", + "* Funkcja kosztu dla regresji:\n", + "$$J(\\Theta) = \\dfrac{1}{2m} \\sum_{i=1}^{m} (h_\\Theta(x^{(i)})- y^{(i)})^2 $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Jak obliczymy gradienty?\n", + "\n", + "$$\\nabla_{\\Theta^{(l)}} J(\\Theta) = ? \\quad \\nabla_{\\beta^{(l)}} J(\\Theta) = ?$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### W kierunku propagacji wstecznej\n", + "\n", + "* Pewna (niewielka) zmiana wagi $\\Delta z^l_j$ dla $j$-ego neuronu w warstwie $l$ pociąga za sobą (niewielką) zmianę kosztu: \n", + "\n", + "$$\\frac{\\partial J(\\Theta)}{\\partial z^{l}_j} \\Delta z^{l}_j$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Jeżeli $\\frac{\\partial J(\\Theta)}{\\partial z^{l}_j}$ jest duża, $\\Delta z^l_j$ ze znakiem przeciwnym zredukuje koszt.\n", + "* Jeżeli $\\frac{\\partial J(\\Theta)}{\\partial z^l_j}$ jest bliska zeru, koszt nie będzie mocno poprawiony." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Definiujemy błąd $\\delta^l_j$ neuronu $j$ w warstwie $l$: \n", + "\n", + "$$\\delta^l_j \\equiv \\dfrac{\\partial J(\\Theta)}{\\partial z^l_j}$$ \n", + "$$\\delta^l \\equiv \\nabla_{z^l} J(\\Theta) \\textrm{ (zapis wektorowy)} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Podstawowe równania propagacji wstecznej\n", + "\n", + "$$\n", + "\\begin{array}{ccll}\n", + "\\delta^L & = & \\nabla_{a^L}J(\\Theta) \\odot {(g^{L})}^{\\prime}(z^L) & (BP1) \\\\[2mm]\n", + "\\delta^{l} & = & ((\\Theta^{l+1})^T \\delta^{l+1}) \\odot {{(g^{l})}^{\\prime}}(z^{l}) & (BP2)\\\\[2mm]\n", + "\\nabla_{\\beta^l} J(\\Theta) & = & \\delta^l & (BP3)\\\\[2mm]\n", + "\\nabla_{\\Theta^l} J(\\Theta) & = & a^{l-1} \\odot \\delta^l & (BP4)\\\\\n", + "\\end{array}\n", + "$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Algorytm propagacji wstecznej" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Dla jednego przykładu (x,y):\n", + "\n", + "1. **Wejście**: Ustaw aktywacje w warstwie cech $a^{(0)}=x$ \n", + "2. **Feedforward:** dla $l=1,\\dots,L$ oblicz \n", + "$$z^{(l)} = a^{(l-1)} \\Theta^{(l)} + \\beta^{(l)} \\textrm{ oraz } a^{(l)}=g^{(l)}(z^{(l)})$$\n", + "3. **Błąd wyjścia $\\delta^{(L)}$:** oblicz wektor $$\\delta^{(L)}= \\nabla_{a^{(L)}}J(\\Theta) \\odot {g^{\\prime}}^{(L)}(z^{(L)})$$\n", + "4. **Propagacja wsteczna błędu:** dla $l = L-1,L-2,\\dots,1$ oblicz $$\\delta^{(l)} = \\delta^{(l+1)}(\\Theta^{(l+1)})^T \\odot {g^{\\prime}}^{(l)}(z^{(l)})$$\n", + "5. **Gradienty:** \n", + " * $\\dfrac{\\partial}{\\partial \\Theta_{ij}^{(l)}} J(\\Theta) = a_i^{(l-1)}\\delta_j^{(l)} \\textrm{ oraz } \\dfrac{\\partial}{\\partial \\beta_{j}^{(l)}} J(\\Theta) = \\delta_j^{(l)}$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "W naszym przykładzie:\n", + "\n", + "$$\\small J(\\Theta) = \\frac{1}{2}(a^{(L)} - y)^2 $$\n", + "$$\\small \\dfrac{\\partial}{\\partial a^{(L)}} J(\\Theta) = a^{(L)} - y$$\n", + "\n", + "$$\\small \\tanh^{\\prime}(x) = 1 - \\tanh^2(x)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Algorytm SGD z propagacją wsteczną\n", + "\n", + "Pojedyncza iteracja:\n", + "* Dla parametrów $\\Theta = (\\Theta^{(1)},\\ldots,\\Theta^{(L)})$ utwórz pomocnicze macierze zerowe $\\Delta = (\\Delta^{(1)},\\ldots,\\Delta^{(L)})$ o takich samych wymiarach (dla uproszczenia opuszczono wagi $\\beta$).\n", + "* Dla $m$ przykładów we wsadzie (_batch_), $i = 1,\\ldots,m$:\n", + " * Wykonaj algortym propagacji wstecznej dla przykładu $(x^{(i)}, y^{(i)})$ i przechowaj gradienty $\\nabla_{\\Theta}J^{(i)}(\\Theta)$ dla tego przykładu;\n", + " * $\\Delta := \\Delta + \\dfrac{1}{m}\\nabla_{\\Theta}J^{(i)}(\\Theta)$\n", + "* Wykonaj aktualizację wag: $\\Theta := \\Theta - \\alpha \\Delta$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Propagacja wsteczna – podsumowanie\n", + "\n", + "* Algorytm pierwszy raz wprowadzony w latach 70. XX w.\n", + "* W 1986 David Rumelhart, Geoffrey Hinton i Ronald Williams pokazali, że jest znacznie szybszy od wcześniejszych metod.\n", + "* Obecnie najpopularniejszy algorytm uczenia sieci neuronowych." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 5.5. Implementacja sieci neuronowych" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "

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    \n", + "
    " + ], + "text/plain": [ + " łod.dł. łod.sz. pł.dł. pł.sz. Iris setosa?\n", + "0 5.2 3.4 1.4 0.2 1.0\n", + "1 5.1 3.7 1.5 0.4 1.0\n", + "2 6.7 3.1 5.6 2.4 0.0\n", + "3 6.5 3.2 5.1 2.0 0.0\n", + "4 4.9 2.5 4.5 1.7 0.0\n", + "5 6.0 2.7 5.1 1.6 0.0" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas\n", + "src_cols = ['łod.dł.', 'łod.sz.', 'pł.dł.', 'pł.sz.', 'Gatunek']\n", + "trg_cols = ['łod.dł.', 'łod.sz.', 'pł.dł.', 'pł.sz.', 'Iris setosa?']\n", + "data = (\n", + " pandas.read_csv('iris.csv', usecols=src_cols)\n", + " .apply(lambda x: [x[0], x[1], x[2], x[3], 1 if x[4] == 'Iris-setosa' else 0], axis=1))\n", + "data.columns = trg_cols\n", + "data[:6]" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[ 1. 5.2 3.4 1.4 0.2]\n", + " [ 1. 5.1 3.7 1.5 0.4]\n", + " [ 1. 6.7 3.1 5.6 2.4]\n", + " [ 1. 6.5 3.2 5.1 2. ]\n", + " [ 1. 4.9 2.5 4.5 1.7]\n", + " [ 1. 6. 2.7 5.1 1.6]]\n", + "[[ 1.]\n", + " [ 1.]\n", + " [ 0.]\n", + " [ 0.]\n", + " [ 0.]\n", + " [ 0.]]\n" + ] + } + ], + "source": [ + "m, n_plus_1 = data.values.shape\n", + "n = n_plus_1 - 1\n", + "Xn = data.values[:, 0:n].reshape(m, n)\n", + "X = np.matrix(np.concatenate((np.ones((m, 1)), Xn), axis=1)).reshape(m, n_plus_1)\n", + "Y = np.matrix(data.values[:, n]).reshape(m, 1)\n", + "\n", + "print(X[:6])\n", + "print(Y[:6])" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Using TensorFlow backend.\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 1/10\n", + "150/150 [==============================] - 0s - loss: 2.0678 - acc: 0.6667 \n", + "Epoch 2/10\n", + "150/150 [==============================] - 0s - loss: 1.9711 - acc: 0.6667 \n", + "Epoch 3/10\n", + "150/150 [==============================] - 0s - loss: 1.8811 - acc: 0.6667 \n", + "Epoch 4/10\n", + "150/150 [==============================] - 0s - loss: 1.7793 - acc: 0.6667 \n", + "Epoch 5/10\n", + "150/150 [==============================] - 0s - loss: 1.6948 - acc: 0.6667 \n", + "Epoch 6/10\n", + "150/150 [==============================] - 0s - loss: 1.5993 - acc: 0.6667 \n", + "Epoch 7/10\n", + "150/150 [==============================] - 0s - loss: 1.5162 - acc: 0.6667 \n", + "Epoch 8/10\n", + "150/150 [==============================] - 0s - loss: 1.4308 - acc: 0.6667 \n", + "Epoch 9/10\n", + "150/150 [==============================] - 0s - loss: 1.3487 - acc: 0.6667 \n", + "Epoch 10/10\n", + "150/150 [==============================] - 0s - loss: 1.2676 - acc: 0.6667 \n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from keras.models import Sequential\n", + "from keras.layers import Dense\n", + "\n", + "model = Sequential()\n", + "model.add(Dense(3, input_dim=5))\n", + "model.add(Dense(3))\n", + "model.add(Dense(1, activation='sigmoid'))\n", + "\n", + "model.compile(loss='binary_crossentropy', optimizer='adam', metrics=['accuracy'])\n", + "\n", + "model.fit(X, Y)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.8209257125854492" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.predict(np.array([1.0, 3.0, 1.0, 2.0, 4.0]).reshape(-1, 5)).tolist()[0][0]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 5.6. Funkcje aktywacji" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "* Każda funkcja aktywacji ma swoje zalety i wady.\n", + "* Różne rodzaje funkcji aktywacji nadają się do różnych zastosowań." + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "import math\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import random\n", + "\n", + "import keras\n", + "from keras.datasets import mnist\n", + "from keras.models import Sequential\n", + "from keras.layers import Dense, Dropout, SimpleRNN, LSTM\n", + "from keras.optimizers import Adagrad, Adam, RMSprop, SGD\n", + "\n", + "from IPython.display import YouTubeVideo" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def plot(fun):\n", + " x = np.arange(-3.0, 3.0, 0.01)\n", + " y = [fun(x_i) for x_i in x]\n", + " fig = plt.figure(figsize=(14, 7))\n", + " ax = fig.add_subplot(111)\n", + " fig.subplots_adjust(left=0.1, right=0.9, bottom=0.1, top=0.9)\n", + " ax.set_xlim(-3.0, 3.0)\n", + " ax.set_ylim(-1.5, 1.5)\n", + " ax.grid()\n", + " ax.plot(x, y)\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Funkcja logistyczna" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$ g(x) = \\frac{1}{1 + e^{-x}} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Przyjmuje wartości z przedziału $(0, 1)$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Funkcja logistyczna – wykres" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "data": { + "image/png": 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WN/GR7+qaC7Fr2huodPp6SZK0zBhnkjKhe2ic508P8vypQV44PchzpwZ58fQQ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\nxpkkSZIkZYBxJkmSJEkZYJx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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(lambda x: 1 / (1 + math.exp(-x)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Tangens hiperboliczny" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$ g(x) = \\tanh x = \\frac{e^{x} - e^{-x}}{e^{x} + e^{-x}} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Przyjmuje wartości z przedziału $(-1, 1)$.\n", + "* Powstaje z funkcji logistycznej przez przeskalowanie i przesunięcie." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Tangens hiperboliczny – wykres" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "data": { + "image/png": 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g83bUxMJsZ21AT94yTuMJMwBAgiTyY423S+orqdRau0aSjDGLJK2WdIekhw61\noTFmhKRrJN1irX08vux9SUsl/UrSRQmcGwAASdL2miZdPWW2KuuDeurWcRrdq8DpkQAASSyRH2u8\nSNLsPWEmSdba9ZI+knRxK7YNSfrbftuGJf1V0jnGmNS2HxcAgH12NUV15SOztYswAwAcI4mMsyGS\nlrSwfKmkwa3Ydr21trGFbf2S+h/9eAAAtGzL7kY9MDeg3Y1BTb9tvI4vyXd6JABAB5DIjzUWSNrd\nwvIqSV/2W+6Ltt3z+gGMMZMlTZakwsJClZWVtXpQdAz19fXsF2gR+wb2V9EY1QNzA2oMRXXPuFRV\nr/1MZWudngpuwt8ZaAn7BdpC0lxK31o7RdIUSSotLbUTJ050diC4TllZmdgv0BL2DeyxaVejfjp1\ntsImRT8c59VNF5/h9EhwIf7OQEvYL9AWEvmxxt1q+QjZoY6KtXZbad8RNAAA2sTGXQ26asosNQTD\neua28eqd63V6JABAB5PIOFuq2LljBxssaVkrtu0Tvxz/wdsGJa35/CYAAByZ9ZUNuvKR2WoKRfTs\nbRM0tHuu0yMBADqgRMbZK5ImGGP67llgjOkt6aT4a1/kVUk+SZfvt22KpCslvWWtbW7rYQEAHdPa\ninpdNWWWgpGonr19ggZ3y3F6JABAB5XIOJsqaYOkfxhjLjbGXCTpH5I2S3pkz0rGmF7GmLAx5j/3\nLLPWLlDsMvp/MMbcZow5Q7HL6PeR9IsEzgwA6EDWlNfr6imzFY5Yzbh9ggZ1JcwAAM5JWJxZaxsk\nnS5plaTpkp6RtF7S6dba+v1WNZK8Lcxys6THJd0v6XVJPSWda62dn6iZAQAdx5ryOl01Zbai1mrG\n5AkqLc52eiQAQAeX0Ks1Wms3Sbr0S9bZoFigHby8SdL34jcAANrMqp11umbqbBljNOP2CepfRJgB\nAJyXyI81AgDgOit21OrqKbPlMUZ/nUyYAQDcgzgDAHQYy7bV6pqpc5TijYVZv8Isp0cCAGCvpPkS\nagAAvsjSbTW67tE5SvN5NeP2CerdOdPpkQAAOABHzgAASW/J1hpd++gcpfu8+utkwgwA4E7EGQAg\nqS3cXK1rps5Wpj9Ff518gnp1IswAAO5EnAEAktb8Tbt13aNzlJvh018nT1BJpwynRwIA4JA45wwA\nkJQ+3VClmx7/RJ2y/Jpx+wR1y0t3eiQAAL4QR84AAElnzrpdumHaXBVlp+pvk08gzAAA7QJHzgAA\nSeXjNZW69clP1T0/Xc/eNl5FOWlOjwQAQKtw5AwAkDRmrq7QzU98opKCDM24fQJhBgBoVzhyBgBI\nCu+tLNcd0+epb+dMPXPbeHXQ4YzWAAAfa0lEQVTKSnV6JAAADgtxBgBo995ZtlN3PjNfA7pk6elb\nxys/0+/0SAAAHDY+1ggAaNfeXLJD33hmngZ1zdazt00gzAAA7RZHzgAA7dYbi7fr7hkLNKxHrp68\nZZxy0nxOjwQAwBHjyBkAoF16ZeE2fWvGAo3smaenCDMAQBLgyBkAoN15acEW/cdzCzWmd4Eev2ms\nMlP5dQYAaP84cgYAaFeenbNJ33tuoSb07aQnbibMAADJg99oAIB249GZ63T/68t1+sAiPXzt8Urz\neZ0eCQCANkOcAQBcz1qrP/17jR56e5W+MqxYf7hylPwpfPgDAJBciDMAgKtZa/Xgmyv1f++v1deO\n765fXzpcKV7CDACQfIgzAIBrRaNW9766VE/O2qhrx5fovouHyuMxTo8FAEBCEGcAAFeKRK1+9PdF\nen7eFt1+Sh/95CuDZAxhBgBIXsQZAMB1QpGovvu3z/Taou369hkD9J0zBxBmAICkR5wBAFwlEIro\nrmfn653l5frxeQN1x2n9nB4JAIBjgjgDALhGQ3NYd0yfpw/XVOq+i4fo+hN6Oz0SAADHDHEGAHCF\n3Q1B3fzEJ1q0pVq/uWy4Lh/T0+mRAAA4pogzAIDjdtQEdP1jc7SxqlH/e91onTOk2OmRAAA45ogz\nAICj1lc26LpH56imKaQnbh6rE/t1dnokAAAcQZwBAByzZGuNbpw2V1bSjNsnaFiPXKdHAgDAMcQZ\nAMARc9bt0m1PfqqcdJ+eunWc+hVmOT0SAACOIs4AAMfc28t26q5n56tnQYaeumWcuuWlOz0SAACO\nI84AAMfU3+dt0T1/X6Sh3XL0+M3jVJDpd3okAABcgTgDABwzj85cp/tfX66T+nfSI9ePUVYqv4YA\nANiD34oAgISz1urX/1qp/y1bq/OGFusPV41UaorX6bEAAHAV4gwAkFDBcFQ//PsivbRgq64ZX6L7\nLh4qr8c4PRYAAK5DnAEAEqYuENI3np6vD9dU6gfnlOrOif1kDGEGAEBLiDMAQELsrA3oxmlztaa8\nXr+9fIQuG93D6ZEAAHA14gwA0OZW76zTTY9/ourGoKbdNFanHlfo9EgAALgecQYAaFNz11fptic/\nUarPq7/dcYKGds91eiQAANoF4gwA0GbeWLxd3/nbZ+qRn64nbx6nngUZTo8EAEC7QZwBAI6atVaP\nfbhe//XGch1fkq9HbxijfL5cGgCAw0KcAQCOSigS1S9eWapn52zSeUOL9fsrRyrNx3eYAQBwuIgz\nAMARq2kK6a5n52vm6kp9Y2I//eDsUnn4DjMAAI4IcQYAOCKbdjXqlic/0YbKBv36suG6YkxPp0cC\nAKBdI84AAIft0w1Vmjx9niJRq+m3jtcJ/To5PRIAAO0ecQYAOCwvL9iqe15YpO756XrsxjHqW5jl\n9EgAACQF4gwA0CrWWv3+ndX6n3dXa3yfAv3fdaO5IiMAAG2IOAMAfKnGYFj3vLBIry3arstG99D/\nu2SY/Ckep8cCACCpEGcAgC+0ZXejJj81T8t31OqH5w7U10/rK2O4IiMAAG2NOAMAHNLsdbt05zPz\nFYpENe3GsZo0sMjpkQAASFrEGQDgc6y1enrOJt37ylKVdMrQ1BvGqB8X/gAAIKGIMwDAAYLhqH7x\nylLNmLtJpw8s0h+uGqmcNJ/TYwEAkPSIMwDAXuV1Ad359Hx9unG37pzYT/9xdqm8Hs4vAwDgWCDO\nAACSpLnrq/TNZ+erLhDSn64epQtHdHN6JAAAOpSEXQfZGOMxxvzYGLPBGBMwxiw0xlzaym2fMMbY\nFm5/SNS8ANBRWWv16Mx1unrqbGX6vXr5mycRZgAAOCCRR87uk/R9ST+VNE/SVZKeN8ZcYK19oxXb\nV0i66KBl29t2RADo2Oqbw/rhC4v0+uLtOntwF/32ihGcXwYAgEMSEmfGmCLFwuwBa+1v44vfM8b0\nl/SApNbEWdBaOzsR8wEApNU763TH0/O0obJBPz5voCafyveXAQDgpEQdOTtHkl/S0wctf1rSNGNM\nH2vt+gT9bADAl3hl4Tb96O+LlOH36pnbJuiEfp2cHgkAgA4vUeecDZHULGnNQcuXxu8Ht+I9iowx\nlcaYsDFmlTHmh8YYb5tOCQAdTCAU0U9eWqy7ZyzQ4K45ev3uUwgzAABcwlhr2/5NjZki6SJrbfFB\ny/tLWi3pBmvt9C/Y/juSIorFXJqkSyTdKmmatfa2Q2wzWdJkSSosLBz93HPPtcUfBUmkvr5eWVl8\niS4+r6PsG9vqo3r4s4C21Ft9pY9PXxvgUwqXyT+kjrJf4PCxb6Al7BdoyaRJk+ZZa8e0dv1WfazR\nGHOmpLdbser71tqJrf3hh2KtPfiqjG8YY+olfccY86C1dnUL20yRNEWSSktL7cSJRz0GkkxZWZnY\nL9CSZN83rLV6ft4W3ffuUmX4fXri5hGaWFrk9Fiul+z7BY4c+wZawn6BttDac84+ljSoFes1xu93\nS8ozxhh74KG5gvh9VSt/7v5mSPqOpDGKHX0DAHyJ+uawfvbSYr382Tad0LeT/nDVSHXJSXN6LAAA\n0IJWxZm1tlHSisN436WSUiX104Hnne0512zZYbzX58Y5im0BoMNYsrVG35qxQBt3Neh7Zx2nb07q\nLy8fYwQAwLUSdUGQNyWFJF170PLrJC05wis1XqtYmH1ylLMBQFKLRK3+t2ytLnn4IzUFI5px+wTd\nfcYAwgwAAJdLyKX0rbXlxpiHJP3YGFMnab6kKyWdroO+WNoY866kXtba/vHnvSRNl/RXxY66pSp2\nQZCbJD1irV2biJkBIBlsrmrUfzy3UHM3VOkrw4r1X18dpvxMv9NjAQCAVkjU95xJ0k8l1Uv6tqRi\nSSslXWGtfe2g9bwHzVGn2DlpP5TURVJUsY9U3i3p4QTOCwDtlrVWL87fql+8EvvGkt9dPkJfO747\nXyoNAEA7krA4s9ZGJN0fv33RehMPel4l6auJmgsAkk11Y1A/fWmJXl+8XWN75+uhK0aqZ0GG02MB\nAIDDlMgjZwCABCtbWa4f/n2RqhqCuufcUt1xaj/OLQMAoJ0izgCgHappCun+15bp+XlbNKAoS4/d\nOFZDu+c6PRYAADgKxBkAtDPvLt+pn7y0WJX1QX1zUj/dfcYApaZ4nR4LAAAcJeIMANqJ6sagfvXq\nMr24YKtKu2Tr0RvGalgPjpYBAJAsiDMAaAfeWrpDP315iXY3BHX3GQN016T+8qck6qsqAQCAE4gz\nAHCxHTUB3fvqUv1zyQ4N6pqjx2/i3DIAAJIVcQYALhSJWk2ftUG/fWuVQpGofnBOqW4/pS9HywAA\nSGLEGQC4zJKtNfrJS4u1aEuNThnQWfd/dah6dcp0eiwAAJBgxBkAuER9c1gPvbVKT3y8XgWZqfqf\nq0fpwuFdZQzfWwYAQEdAnAGAw6y1enXRdv2/15drR21A144v0T3nDlRuus/p0QAAwDFEnAGAg5Zu\nq9G9ryzT3A1VGto9R3+59niN7pXv9FgAAMABxBkAOGB3Q1C/e3ulnp2zSXkZfv3314bpijE95fXw\nEUYAADoq4gwAjqFwJKoZczfpt2+tUn1zWDec0FvfPfM45WbwEUYAADo64gwAjgFrrcpWVui//7lc\nq3bW68R+nfSLC4eotDjb6dEAAIBLEGcAkGCLtlTrv99YoVnrdql3pwz933XH65whxVyFEQAAHIA4\nA4AE2VzVqN/8a6VeWbhNBZl+3XvREF0zvkQ+L18kDQAAPo84A4A2VtUQ1MPvrdFTszbK45HumtRf\nd5zWV9lpnFcGAAAOjTgDgDZS0xTSozPXadqH69UUiujy0T313bOOU3FumtOjAQCAdoA4A4CjVBcI\n6fGPNmjqzHWqC4R1/rCu+s6ZAzSgCxf7AAAArUecAcARagyG9eTHG/XIB2tV3RjSWYO76LtnHqfB\n3XKcHg0AALRDxBkAHKbaQEhPz96oaR+uV2V9UBNLC/W9s47T8B55To8GAADaMeIMAFppV32zHv9o\ng56ctUF1gbBOPa5Q3z6jv0b3KnB6NAAAkASIMwD4EtuqmzR15jrNmLtJzeGozhtarDsn9tfQ7rlO\njwYAAJIIcQYAh7BiR60em7leL3+2VdZKXx3VXV8/rZ/6F2U5PRoAAEhCxBkA7CcatXp/dYUem7le\nH66pVJrPo6vHlWjyqX3VIz/D6fEAAEASI84AQFJTMKIXF2zRtA/Xa21Fg7rkpOqec0t1zbgS5WX4\nnR4PAAB0AMQZgA5tc1Wjnl8Z1Hc/eFe7G0Ma2j1Hf7hypL4yrKv8KR6nxwMAAB0IcQagw4lErcpW\nluvp2RtVtqpCstLZQ7rolpP6aFyfAhljnB4RAAB0QMQZgA6joq5Zz326Wc/O2aSt1U0qyk7Vt04f\noN6RLfrauWOcHg8AAHRwxBmApBaORFW2skLPz9usf68oVyhidVL/TvrZ+YN05uAu8nk9Kivb5vSY\nAAAAxBmA5LSmvE7Pf7pFf5+/VZX1zeqc5deNJ/TW1eNL1K+QS+EDAAD3Ic4AJI3dDUG9vni7Xpi3\nRZ9trlaKx2jSwCJdPrqHJg0sks/LBT4AAIB7EWcA2rWG5rDeXrZT//hsq2aurlQ4anVclyz97PxB\n+uqo7uqcler0iAAAAK1CnAFod5rDEZWtrNArC7fp3eU7FQhF1S03Tbee3EcXjuimId1yuOIiAABo\nd4gzAO1CIBTRh6sr9ebSHfrX0h2qC4TVKdOvy0f31MUju+n4knx5PAQZAABov4gzAK5V0xTSeyvK\n9dayHSpbWaHGYETZaSk6e3CxLhrZTSf166QUziMDAABJgjgD4Co7awN6a9lOvbV0h2at3aVw1Koo\nO1WXjOquc4YUa0LfTvKnEGQAACD5EGcAHBWORDV/U7XKVparbGWFlm2vlST16ZypW0/po3OGFGtk\njzw+sggAAJIecQbgmCuvDahsVYXeX1mhmasrVBsIy+sxGl2Srx+cU6qzBnfRgKIsLuoBAAA6FOIM\nQMLVN4f1yfoqfby2Uh+t2bX36FhRdqrOHVqsiaVFOql/Z+Wm+xyeFAAAwDnEGYA2FwhFNG/jbn28\ntlKz1u7Swi01ikSt/F6PRpXk6QfnlGpSaZEGdc3m6BgAAEAccQbgqNUGQlqwqVqfbqjSJxuqNH9j\ntYKRqLweo+E9cvX10/rqxH6dNbpXvtJ8XqfHBQAAcCXiDMBh21rdpE83VOnTDbv1yYYqrdxZJ2sl\nj5EGd8vRjSf20on9OmtsnwJlpfLXDAAAQGvwryYAX6g2ENLiLTVauKVaizbH7rfXBCRJmX6vju+V\nr3OHFmtMrwKNLMkjxgAAAI4Q/4oCsFcgFNHSbTVauLlGi7ZUa9GWGq2rbNj7eq9OGRrTu0BjeuVr\ndK98DSzO5kugAQAA2ghxBnRQFXXNWr69Vsu312rFjjot316r1eX1ikStpNiVFIf3yNMlo7prRM88\nDe+Rq7wMv8NTAwAAJC/iDEhygVBE6yoatGLHvghbvr1WlfXBvesU56RpUNdsnTGoSMN75GlEjzwV\n56Y5ODUAAEDHQ5wBSaKmMaQ1FfVaW16vNRX1WlMeu23e3SgbOxgmf4pHx3XJ0sTSIg3qmqNBXbM1\nqDhH+ZkcEQMAAHAacQa0I4FQRFt2N2rjrthtXeWeCGtQZX3z3vX8KR717ZypYT1y9dVR3dW/KEsD\ni7PVt3Mm54gBAAC4FHEGuExNU0ibdjVqY1VDPMJi95uqGrWjNrD3KJgkZaelqH9RliaVFqp/UZb6\nF2WpX2GWehZkyOvhy50BAADaE+IMOIbCkajK65q1rbpJW6ubtK06oG3VTfs9b1JtIHzANp2zUtWr\nU4ZO6NtJJZ0y1KtThkoKMtWrU4Y6ZfplDBEGAACQDIgzoI00BsMqr21WeV2zdtYGVF7XrPK6gHbU\n7AmwgHbUBvZeDXGP3HSfuuWlq0d+usb1KVD3vHT16pQZj7AMZfK9YQAAAB0C/+oDvkBzOKKqhqB2\n1QdV1RC7VcSja/8Iq6htVl1z+HPb+70eFeWkqnteusb3KVC3vPT4LU3d89LVNS+dL20GAACAJOIM\nHUgkarWrvlk1TSHVNIVU3RRSVTy6djUEVdXQvPfxnhirbyG4JCnN51FRdpqKslM1sDhbpw4oVFFO\nqoqy09Qlfl+Unaq8DB8fOwQAAECrJCzOjDHfkzRJ0hhJxZLutdb+8jC2P1nSryWNklQj6VlJP7XW\nNrX9tGgPIlGrhmBY9YGw6pvjt0B4b2ztvTXuia+gaprCqo0vr28OS2+90+J7+7xGBZl+FWSmqlOm\nXyUlGSrI9KtTfFlBpl+dsvwqyPSrc1aqctJSiC4AAAC0qUQeObtdUq2klyV9/XA2NMYMl/S2pH9J\nukBSH0m/kdRd0pVtOyYSwVqr5nBUTcGImkIRNQYjCoT2PW4KRtQYDKuhOay65s8H197H+z1vDEa+\n9Of6UzzKS/cpN92nvAyfuufFvlw5L92v3Tu3aMSgAcrN8Ckv3a+cdF8svrL8yk4ltgAAAOCsRMbZ\nEGtt1BiTosOMM0n3Stoi6XJrbUiSjDFBSU8aYx601s5v41mTWjRqFYxE1RyOqjkcUTAcfxyKxpaH\nIvH72PJgJLLv8X7bBMJRNQbDagpG1RQK7w2vzwVY/PlB1734Qikeo6y0FGWl7rsVZPrVsyBD2fHn\nmakpyk7b93jP+rnxGMtN9ynN5z3kzygrK9fEk/q0wX+iAAAAQNtLWJxZa6NHsp0xxifpXEkP7Qmz\nuOckTZV0saSExJm1VpGoVThqFY0/jkalcDSqiN33OBqVItYqEo0qEo193C4StfFl+25RG3uvUDiq\ncDSqUMTG7sNWoWhU4YhVKBJfHokqFI3fR/atG47Ewiq8Z9v4Nnu2DUcPeo9IdF98xeMqGDmi/yoO\nYIyUluJVht+rNF/sPj3+OD/Tr26+2PN0X+yW4fcqze9Vhm/fehn+lNjr/n3r7Ams1BQPR64AAADQ\nobnxgiD9JKVJWrL/QmttwBizVtLgL3uDrfVRnfnQ+4rGgykc2RdbXxRR9jCO9CSKz2uU4vEoxWvk\n83qU4ond+7xGKfHn/pTYfYrXozSfR9lpKUrxxNbxeT1KTfHIn+JRaopXqT6P/F6PUn2x57Hl+9+8\nrVo/xWOIJwAAACCB3BhnBfH73S28VrXf64fk8xgd1yVLHmOU4jHyeIy8xijFa+QxRl5P/Lb/Y89B\nrx30uscTey+v2ffY87n3UPxneuTxaO/PjEXWvng6ILxSPPLFY4wAAgAAADquVsWZMeZMxS7Q8WXe\nt9ZOPKqJjpAxZrKkyZJUWFioK7rXHd0b2vjtCD4R2PLF1+G0+vp6lZWVOT0GXIh9Ay1hv8ChsG+g\nJewXaAutPXL2saRBrViv8Shm2WPPEbP8Fl4rkLS0pY2stVMkTZGk0tJSO3HixDYYBcmkrKxM7Bdo\nCfsGWsJ+gUNh30BL2C/QFloVZ9baRkkrEjzLHmslNUsasv9CY0yapL6Snj9GcwAAAADAMeNxeoCD\nWWuDkt6UdEX8Mvx7XCYpVdIrjgwGAAAAAAmUsAuCGGPGSOqtfQE42BhzWfzxG/GjcTLGPCbpRmvt\n/rP8UtJsSc8ZY/4Sf5/fSHrBWjsvUTMDAAAAgFMSebXGuyTduN/zy+M3SeojaUP8sTd+28ta+5kx\n5mxJD0p6XVKNpKck/SSB8wIAAACAYxL5JdQ3SbrpSNez1n4g6YQ2HgsAAAAAXMl155wBAAAAQEdE\nnAEAAACACxBnAAAAAOACxBkAAAAAuABxBgAAAAAuQJwBAAAAgAsQZwAAAADgAsQZAAAAALgAcQYA\nAAAALkCcAQAAAIALEGcAAAAA4ALEGQAAAAC4AHEGAAAAAC5AnAEAAACACxBnAAAAAOACxBkAAAAA\nuABxBgAAAAAuQJwBAAAAgAsQZwAAAADgAsQZAAAAALgAcQYAAAAALkCcAQAAAIALEGcAAAAA4ALE\nGQAAAAC4AHEGAAAAAC5AnAEAAACACxBnAAAAAOACxBkAAAAAuABxBgAAAAAuQJwBAAAAgAsQZwAA\nAADgAsQZAAAAALgAcQYAAAAALkCcAQAAAIALEGcAAAAA4ALEGQAAAAC4AHEGAAAAAC5AnAEAAACA\nCxBnAAAAAOACxBkAAAAAuABxBgAAAAAuQJwBAAAAgAsQZwAAAADgAsQZAAAAALgAcQYAAAAALkCc\nAQAAAIALEGcAAAAA/n979x5iaV3Hcfz9qU2wlMhLEpaulpprEdUGS0WauZp/ZAVbf1QqQZqVYYqU\nhtBamBR5iaUiNTMrumClLpmgmRJ5a0syraytFBeUvItubF6+/fGcyWE6Z3Zmd878npl5v2A4t+c5\n81n2t2ef7/nd1AMWZ5IkSZLUAxZnkiR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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(lambda x: math.tanh(x))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### ReLU (_Rectifier Linear Unit_)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$ g(x) = \\max(0, x) $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### ReLU – zalety\n", + "* Mniej podatna na problem zanikającego gradientu (_vanishing gradient_) niż funkcje sigmoidalne, dzięki czemu SGD jest szybciej zbieżna.\n", + "* Prostsze obliczanie gradientu.\n", + "* Dzięki zerowaniu ujemnych wartości, wygasza neurony, „rozrzedzając” sieć (_sparsity_), co przyspiesza obliczenia." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "#### ReLU – wady\n", + "* Dla dużych wartości gradient może „eksplodować”.\n", + "* „Wygaszanie” neuronów." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### ReLU – wykres" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(lambda x: max(0, x))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Softplus" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "$$ g(x) = \\log(1 + e^{x}) $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Wygładzona wersja ReLU." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Softplus – wykres" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(lambda x: math.log(1 + math.exp(x)))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "### Problem zanikającego gradientu (_vanishing gradient problem_)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Sigmoidalne funkcje aktywacji ograniczają wartości na wyjściach neuronów do niewielkich przedziałów ($(-1, 1)$, $(0, 1)$ itp.).\n", + "* Jeżeli sieć ma wiele warstw, to podczas propagacji wstecznej mnożymy przez siebie wiele małych wartości → obliczony gradient jest mały.\n", + "* Im więcej warstw, tym silniejszy efekt zanikania." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Sposoby na zanikający gradient\n", + "\n", + "* Modyfikacja algorytmu optymalizacji (_RProp_, _RMSProp_)\n", + "* Użycie innej funckji aktywacji (ReLU, softplus)\n", + "* Dodanie warstw _dropout_\n", + "* Nowe architektury (LSTM itp.)\n", + "* Więcej danych, zwiększenie mocy obliczeniowej" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## 5.7. Wielowarstwowe sieci neuronowe w praktyce" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Przykład: MNIST\n", + "\n", + "_Modified National Institute of Standards and Technology database_" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "* Zbiór cyfr zapisanych pismem odręcznym\n", + "* 60 000 przykładów uczących, 10 000 przykładów testowych\n", + "* Rozdzielczość każdego przykładu: 28 × 28 = 784 piksele" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "# źródło: https://github.com/keras-team/keras/examples/minst_mlp.py\n", + "\n", + "import keras\n", + "from keras.datasets import mnist\n", + "\n", + "# załaduj dane i podziel je na zbiory uczący i testowy\n", + "(x_train, y_train), (x_test, y_test) = mnist.load_data()" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [], + "source": [ + "def draw_examples(examples, captions=None):\n", + " plt.figure(figsize=(16, 4))\n", + " m = len(examples)\n", + " for i, example in enumerate(examples):\n", + " plt.subplot(100 + m * 10 + i + 1)\n", + " plt.imshow(example, cmap=plt.get_cmap('gray'))\n", + " plt.show()\n", + " if captions is not None:\n", + " print(6 * ' ' + (10 * ' ').join(str(captions[i]) for i in range(m)))" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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PlAvF+LgV48+UC8X2uBXbz5Mrxfi4FePPlAvF+LgV48+UC8X2uBXbz5MrcX/c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\nWPn/0DbqrzfbMFoAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + " 5 0 4 1 9 2 1\n" + ] + } + ], + "source": [ + "draw_examples(x_train[:7], captions=y_train)" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "60000 przykładów uczących\n", + "10000 przykładów testowych\n" + ] + } + ], + "source": [ + "num_classes = 10\n", + "\n", + "x_train = x_train.reshape(60000, 784) # 784 = 28 * 28\n", + "x_test = x_test.reshape(10000, 784)\n", + "x_train = x_train.astype('float32')\n", + "x_test = x_test.astype('float32')\n", + "x_train /= 255\n", + "x_test /= 255\n", + "print('{} przykładów uczących'.format(x_train.shape[0]))\n", + "print('{} przykładów testowych'.format(x_test.shape[0]))\n", + "\n", + "# przekonwertuj wektory klas na binarne macierze klas\n", + "y_train = keras.utils.to_categorical(y_train, num_classes)\n", + "y_test = keras.utils.to_categorical(y_test, num_classes)" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "_________________________________________________________________\n", + "Layer (type) Output Shape Param # \n", + "=================================================================\n", + "dense_4 (Dense) (None, 512) 401920 \n", + "_________________________________________________________________\n", + "dropout_1 (Dropout) (None, 512) 0 \n", + "_________________________________________________________________\n", + "dense_5 (Dense) (None, 512) 262656 \n", + "_________________________________________________________________\n", + "dropout_2 (Dropout) (None, 512) 0 \n", + "_________________________________________________________________\n", + "dense_6 (Dense) (None, 10) 5130 \n", + "=================================================================\n", + "Total params: 669,706\n", + "Trainable params: 669,706\n", + "Non-trainable params: 0\n", + "_________________________________________________________________\n" + ] + } + ], + "source": [ + "model = Sequential()\n", + "model.add(Dense(512, activation='relu', input_shape=(784,)))\n", + "model.add(Dropout(0.2))\n", + "model.add(Dense(512, activation='relu'))\n", + "model.add(Dropout(0.2))\n", + "model.add(Dense(num_classes, activation='softmax'))\n", + "model.summary()" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "((60000, 784), (60000, 10))\n" + ] + } + ], + "source": [ + "print(x_train.shape, y_train.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Train on 60000 samples, validate on 10000 samples\n", + "Epoch 1/5\n", + "60000/60000 [==============================] - 14s - loss: 0.2457 - acc: 0.9244 - val_loss: 0.1250 - val_acc: 0.9605\n", + "Epoch 2/5\n", + "60000/60000 [==============================] - 14s - loss: 0.1021 - acc: 0.9691 - val_loss: 0.0859 - val_acc: 0.9748\n", + "Epoch 3/5\n", + "60000/60000 [==============================] - 14s - loss: 0.0746 - acc: 0.9773 - val_loss: 0.0884 - val_acc: 0.9744\n", + "Epoch 4/5\n", + "60000/60000 [==============================] - 13s - loss: 0.0619 - acc: 0.9815 - val_loss: 0.0893 - val_acc: 0.9754\n", + "Epoch 5/5\n", + "60000/60000 [==============================] - 15s - loss: 0.0507 - acc: 0.9849 - val_loss: 0.0845 - val_acc: 0.9771\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 37, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "model.compile(loss='categorical_crossentropy', optimizer=RMSprop(), metrics=['accuracy'])\n", + "\n", + "model.fit(x_train, y_train, batch_size=128, epochs=5, verbose=1,\n", + " validation_data=(x_test, y_test))" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test loss: 0.0845102945257\n", + "Test accuracy: 0.9771\n" + ] + } + ], + "source": [ + "score = model.evaluate(x_test, y_test, verbose=0)\n", + "\n", + "print('Test loss: {}'.format(score[0]))\n", + "print('Test accuracy: {}'.format(score[1]))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Warstwa _dropout_ to metoda regularyzacji, służy zapobieganiu nadmiernemu dopasowaniu sieci. Polega na tym, że część węzłów sieci jest usuwana w sposób losowy." + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "_________________________________________________________________\n", + "Layer (type) Output Shape Param # \n", + "=================================================================\n", + "dense_7 (Dense) (None, 512) 401920 \n", + "_________________________________________________________________\n", + "dense_8 (Dense) (None, 512) 262656 \n", + "_________________________________________________________________\n", + "dense_9 (Dense) (None, 10) 5130 \n", + "=================================================================\n", + "Total params: 669,706\n", + "Trainable params: 669,706\n", + "Non-trainable params: 0\n", + "_________________________________________________________________\n", + "Train on 60000 samples, validate on 10000 samples\n", + "Epoch 1/5\n", + "60000/60000 [==============================] - 11s - loss: 0.2214 - acc: 0.9314 - val_loss: 0.1048 - val_acc: 0.9668\n", + "Epoch 2/5\n", + "60000/60000 [==============================] - 12s - loss: 0.0838 - acc: 0.9739 - val_loss: 0.0842 - val_acc: 0.9752\n", + "Epoch 3/5\n", + "60000/60000 [==============================] - 10s - loss: 0.0548 - acc: 0.9829 - val_loss: 0.0806 - val_acc: 0.9773\n", + "Epoch 4/5\n", + "60000/60000 [==============================] - 9s - loss: 0.0387 - acc: 0.9878 - val_loss: 0.0713 - val_acc: 0.9804\n", + "Epoch 5/5\n", + "60000/60000 [==============================] - 9s - loss: 0.0297 - acc: 0.9911 - val_loss: 0.0847 - val_acc: 0.9787\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Bez warstw Dropout\n", + "\n", + "num_classes = 10\n", + "\n", + "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n", + "\n", + "x_train = x_train.reshape(60000, 784) # 784 = 28 * 28\n", + "x_test = x_test.reshape(10000, 784)\n", + "x_train = x_train.astype('float32')\n", + "x_test = x_test.astype('float32')\n", + "x_train /= 255\n", + "x_test /= 255\n", + "\n", + "y_train = keras.utils.to_categorical(y_train, num_classes)\n", + "y_test = keras.utils.to_categorical(y_test, num_classes)\n", + "\n", + "model_no_dropout = Sequential()\n", + "model_no_dropout.add(Dense(512, activation='relu', input_shape=(784,)))\n", + "model_no_dropout.add(Dense(512, activation='relu'))\n", + "model_no_dropout.add(Dense(num_classes, activation='softmax'))\n", + "model_no_dropout.summary()\n", + "\n", + "model_no_dropout.compile(loss='categorical_crossentropy',\n", + " optimizer=RMSprop(),\n", + " metrics=['accuracy'])\n", + "\n", + "model_no_dropout.fit(x_train, y_train,\n", + " batch_size=128,\n", + " epochs=5,\n", + " verbose=1,\n", + " validation_data=(x_test, y_test))" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test loss (no dropout): 0.0846566448619\n", + "Test accuracy (no dropout): 0.9787\n" + ] + } + ], + "source": [ + "# Bez warstw Dropout\n", + "\n", + "score = model_no_dropout.evaluate(x_test, y_test, verbose=0)\n", + "\n", + "print('Test loss (no dropout): {}'.format(score[0]))\n", + "print('Test accuracy (no dropout): {}'.format(score[1]))" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "slideshow": { + "slide_type": "notes" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "_________________________________________________________________\n", + "Layer (type) Output Shape Param # \n", + "=================================================================\n", + "dense_10 (Dense) (None, 2500) 1962500 \n", + "_________________________________________________________________\n", + "dense_11 (Dense) (None, 2000) 5002000 \n", + "_________________________________________________________________\n", + "dense_12 (Dense) (None, 1500) 3001500 \n", + "_________________________________________________________________\n", + "dense_13 (Dense) (None, 1000) 1501000 \n", + "_________________________________________________________________\n", + "dense_14 (Dense) (None, 500) 500500 \n", + "_________________________________________________________________\n", + "dense_15 (Dense) (None, 10) 5010 \n", + "=================================================================\n", + "Total params: 11,972,510\n", + "Trainable params: 11,972,510\n", + "Non-trainable params: 0\n", + "_________________________________________________________________\n", + "Train on 60000 samples, validate on 10000 samples\n", + "Epoch 1/10\n", + "60000/60000 [==============================] - 212s - loss: 0.7388 - acc: 0.7954 - val_loss: 0.2908 - val_acc: 0.9172\n", + "Epoch 2/10\n", + "60000/60000 [==============================] - 191s - loss: 0.2390 - acc: 0.9305 - val_loss: 0.1833 - val_acc: 0.9470\n", + "Epoch 3/10\n", + "60000/60000 [==============================] - 166s - loss: 0.1688 - acc: 0.9517 - val_loss: 0.1555 - val_acc: 0.9549\n", + "Epoch 4/10\n", + "60000/60000 [==============================] - 166s - loss: 0.1344 - acc: 0.9614 - val_loss: 0.1274 - val_acc: 0.9621\n", + "Epoch 5/10\n", + "60000/60000 [==============================] - 166s - loss: 0.1074 - acc: 0.9683 - val_loss: 0.1213 - val_acc: 0.9661\n", + "Epoch 6/10\n", + "60000/60000 [==============================] - 440s - loss: 0.0924 - acc: 0.9725 - val_loss: 0.1066 - val_acc: 0.9709\n", + "Epoch 7/10\n", + "60000/60000 [==============================] - 169s - loss: 0.0768 - acc: 0.9773 - val_loss: 0.1777 - val_acc: 0.9517\n", + "Epoch 8/10\n", + "60000/60000 [==============================] - 183s - loss: 0.0657 - acc: 0.9805 - val_loss: 0.1053 - val_acc: 0.9711\n", + "Epoch 9/10\n", + "60000/60000 [==============================] - 170s - loss: 0.0572 - acc: 0.9832 - val_loss: 0.1044 - val_acc: 0.9717\n", + "Epoch 10/10\n", + "60000/60000 [==============================] - 166s - loss: 0.0493 - acc: 0.9851 - val_loss: 0.0938 - val_acc: 0.9752\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 41, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Więcej warstw, inna funkcja aktywacji\n", + "\n", + "num_classes = 10\n", + "\n", + "(x_train, y_train), (x_test, y_test) = mnist.load_data()\n", + "\n", + "x_train = x_train.reshape(60000, 784) # 784 = 28 * 28\n", + "x_test = x_test.reshape(10000, 784)\n", + "x_train = x_train.astype('float32')\n", + "x_test = x_test.astype('float32')\n", + "x_train /= 255\n", + "x_test /= 255\n", + "\n", + "y_train = keras.utils.to_categorical(y_train, num_classes)\n", + "y_test = keras.utils.to_categorical(y_test, num_classes)\n", + "\n", + "model3 = Sequential()\n", + "model3.add(Dense(2500, activation='tanh', input_shape=(784,)))\n", + "model3.add(Dense(2000, activation='tanh'))\n", + "model3.add(Dense(1500, activation='tanh'))\n", + "model3.add(Dense(1000, activation='tanh'))\n", + "model3.add(Dense(500, activation='tanh'))\n", + "model3.add(Dense(num_classes, activation='softmax'))\n", + "model3.summary()\n", + "\n", + "model3.compile(loss='categorical_crossentropy',\n", + " optimizer=RMSprop(),\n", + " metrics=['accuracy'])\n", + "\n", + "model3.fit(x_train, y_train,\n", + " batch_size=128,\n", + " epochs=10,\n", + " verbose=1,\n", + " validation_data=(x_test, y_test))" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Test loss: 0.0937788957049\n", + "Test accuracy: 0.9752\n" + ] + } + ], + "source": [ + "# Więcej warstw, inna funkcja aktywacji\n", + "\n", + "score = model3.evaluate(x_test, y_test, verbose=0)\n", + "\n", + "print('Test loss: {}'.format(score[0]))\n", + "print('Test accuracy: {}'.format(score[1]))" + ] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.15rc1" + }, + "livereveal": { + "start_slideshow_at": "selected", + "theme": "amu" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/w5/zumz5.pdf b/w5/zumz5.pdf new file mode 100644 index 0000000000000000000000000000000000000000..469528c47bab0f876da06fa2eea4e7345171a6d5 GIT binary patch literal 58649 zcmb5VcTiJr@Gl&C?@dFI5_<2w*U(D<2?3=gy(*wo 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