Lab1 and preparation of Lab3

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Marek Moryl 2023-05-06 11:27:31 +02:00
parent 7fc7e1b83c
commit 79bca5203f
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w2/plantvillage dataset/

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"## Uczenie maszynowe zastosowania\n",
"### Zajęcia laboratoryjne\n",
"# 3. Regresja liniowa zadanie"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Zadanie 3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Część podstawowa (4 punkty)\n",
"\n",
"Plik `fires_thefts.csv` zawiera rzeczywiste dane zebrane przez *U.S. Commission on Civil Rights*, przedstawiające liczbę pożarów w danej dzielnicy na tysiąc gospodarstw domowych (pierwsza kolumna) oraz liczbę włamań w tej samej dzielnicy na tysiąc mieszkańców (druga kolumna). \n",
"\n",
"Stwórz model (regresja liniowa) przewidujący liczbę włamań na podstawie liczby pożarów:\n",
" * Oblicz parametry $\\theta$ krzywej regresyjnej za pomocą metody gradientu prostego (*gradient descent*). Możesz wybrać wersję iteracyjną lub macierzową algorytmu.\n",
" * Wykorzystując uzyskaną krzywą regresyjną przepowiedz liczbę włamań na tysiąc mieszkańców dla dzielnicy, w której występuje średnio 50, 100, 200 pożarów na tysiąc gospodarstw domowych."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Część zaawansowana (2 punkty)\n",
"\n",
"Dla różnych wartości długości kroku $\\alpha \\in \\{ 0.001, 0.01 , 0.1 \\}$ stwórz wykres, który zilustruje progresję wartości $J(\\theta)$ dla pierwszych 200 króków algorytmu gradientu prostego:\n",
" * Oś $x$ wykresu to kolejne kroki algorytmu od 0 do 200.\n",
" * Oś $y$ wykresu to wartosci $J(\\theta)$.\n",
" * Wykres powinien skłądać się z trzech krzywych:\n",
" 1. dla $\\alpha = 0.001$\n",
" 2. dla $\\alpha = 0.01$\n",
" 3. dla $\\alpha = 0.1$"
]
}
],
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "fc2a6be1",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Predicted amount of thefts for 50 fires: 100.5454538681846\n",
"Predicted amount of thefts for 100 fires: 195.86844057898603\n",
"Predicted amount of thefts for 200 fires: 386.5144140005889\n"
]
}
],
"source": [
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"\n",
"data = pd.read_csv('fires_thefts.csv', names = ['fires', 'thefts'])\n",
"\n",
"x = data[['fires']].to_numpy().flatten()\n",
"y = data[['thefts']].to_numpy().flatten()\n",
"\n",
"def gradient_descent(h, cost_fun, theta, x, y, alpha, eps, max_steps = 1000000):\n",
" current_cost = cost_fun(h, theta, x, y)\n",
" log = [[current_cost, theta]]\n",
" m = len(y)\n",
" steps_counter = 0\n",
" while True and steps_counter < max_steps:\n",
" steps_counter += 1\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\n",
" prev_cost = current_cost\n",
" current_cost = cost_fun(h, theta, x, y)\n",
" if abs(prev_cost - current_cost) <= eps:\n",
" break\n",
" log.append([current_cost, theta])\n",
" return theta, log\n",
"\n",
"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))\n",
"\n",
"def h(theta, x):\n",
" return theta[0] + theta[1] * x\n",
"\n",
"def mse(expected, predicted):\n",
" m = len(expected)\n",
" if len(predicted) != m:\n",
" raise Exception('Wektory mają różne długości!')\n",
" return 1.0 / (2 * m) * sum((expected[i] - predicted[i])**2 for i in range(m))\n",
"\n",
"best_theta, log = gradient_descent(h, J, [0.0, 0.0], x, y, alpha=0.001, eps=0.0000001, max_steps = 200)\n",
"\n",
"predicted_50 = h(best_theta, 50)\n",
"predicted_100 = h(best_theta, 100)\n",
"predicted_200 = h(best_theta, 200)\n",
"print(f'Predicted amount of thefts for 50 fires: {predicted_50}')\n",
"print(f'Predicted amount of thefts for 100 fires: {predicted_100}')\n",
"print(f'Predicted amount of thefts for 200 fires: {predicted_200}')"
]
}
],
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"## Uczenie maszynowe zastosowania\n",
"### Zajęcia laboratoryjne\n",
"# 3. Regresja liniowa zadanie"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Zadanie 3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Część podstawowa (4 punkty)\n",
"\n",
"Plik `fires_thefts.csv` zawiera rzeczywiste dane zebrane przez *U.S. Commission on Civil Rights*, przedstawiające liczbę pożarów w danej dzielnicy na tysiąc gospodarstw domowych (pierwsza kolumna) oraz liczbę włamań w tej samej dzielnicy na tysiąc mieszkańców (druga kolumna). \n",
"\n",
"Stwórz model (regresja liniowa) przewidujący liczbę włamań na podstawie liczby pożarów:\n",
" * Oblicz parametry $\\theta$ krzywej regresyjnej za pomocą metody gradientu prostego (*gradient descent*). Możesz wybrać wersję iteracyjną lub macierzową algorytmu.\n",
" * Wykorzystując uzyskaną krzywą regresyjną przepowiedz liczbę włamań na tysiąc mieszkańców dla dzielnicy, w której występuje średnio 50, 100, 200 pożarów na tysiąc gospodarstw domowych."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Część zaawansowana (2 punkty)\n",
"\n",
"Dla różnych wartości długości kroku $\\alpha \\in \\{ 0.001, 0.01 , 0.1 \\}$ stwórz wykres, który zilustruje progresję wartości $J(\\theta)$ dla pierwszych 200 króków algorytmu gradientu prostego:\n",
" * Oś $x$ wykresu to kolejne kroki algorytmu od 0 do 200.\n",
" * Oś $y$ wykresu to wartosci $J(\\theta)$.\n",
" * Wykres powinien skłądać się z trzech krzywych:\n",
" 1. dla $\\alpha = 0.001$\n",
" 2. dla $\\alpha = 0.01$\n",
" 3. dla $\\alpha = 0.1$"
]
}
],
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l1/data1.csv Normal file
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price,isNew,rooms,floor,location,sqrMetres
476118.0,False,3,1,Centrum,78
459531.0,False,3,2,Sołacz,62
411557.0,False,3,0,Sołacz,15
496416.0,False,4,0,Sołacz,14
406032.0,False,3,0,Sołacz,15
450026.0,False,3,1,Naramowice,80
571229.15,False,2,4,Wilda,39
325000.0,False,3,1,Grunwald,54
268229.0,False,2,1,Grunwald,90
1 price isNew rooms floor location sqrMetres
2 476118.0 False 3 1 Centrum 78
3 459531.0 False 3 2 Sołacz 62
4 411557.0 False 3 0 Sołacz 15
5 496416.0 False 4 0 Sołacz 14
6 406032.0 False 3 0 Sołacz 15
7 450026.0 False 3 1 Naramowice 80
8 571229.15 False 2 4 Wilda 39
9 325000.0 False 3 1 Grunwald 54
10 268229.0 False 2 1 Grunwald 90

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l1/data1.tsv Normal file
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price isNew rooms floor location sqrMetres
476118.0 False 3 1 Centrum 78
459531.0 False 3 2 Sołacz 62
411557.0 False 3 0 Sołacz 15
496416.0 False 4 0 Sołacz 14
406032.0 False 3 0 Sołacz 15
450026.0 False 3 1 Naramowice 80
571229.15 False 2 4 Wilda 39
325000.0 False 3 1 Grunwald 54
268229.0 False 2 1 Grunwald 90
1 price isNew rooms floor location sqrMetres
2 476118.0 False 3 1 Centrum 78
3 459531.0 False 3 2 Sołacz 62
4 411557.0 False 3 0 Sołacz 15
5 496416.0 False 4 0 Sołacz 14
6 406032.0 False 3 0 Sołacz 15
7 450026.0 False 3 1 Naramowice 80
8 571229.15 False 2 4 Wilda 39
9 325000.0 False 3 1 Grunwald 54
10 268229.0 False 2 1 Grunwald 90

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1,14.23,1.71,2.43,15.6,127,2.8,3.06,.28,2.29,5.64,1.04,3.92,1065
1,13.2,1.78,2.14,11.2,100,2.65,2.76,.26,1.28,4.38,1.05,3.4,1050
1,13.16,2.36,2.67,18.6,101,2.8,3.24,.3,2.81,5.68,1.03,3.17,1185
1,14.37,1.95,2.5,16.8,113,3.85,3.49,.24,2.18,7.8,.86,3.45,1480
1,13.24,2.59,2.87,21,118,2.8,2.69,.39,1.82,4.32,1.04,2.93,735
1,14.2,1.76,2.45,15.2,112,3.27,3.39,.34,1.97,6.75,1.05,2.85,1450
1,14.39,1.87,2.45,14.6,96,2.5,2.52,.3,1.98,5.25,1.02,3.58,1290
1,14.06,2.15,2.61,17.6,121,2.6,2.51,.31,1.25,5.05,1.06,3.58,1295
1,14.83,1.64,2.17,14,97,2.8,2.98,.29,1.98,5.2,1.08,2.85,1045
1,13.86,1.35,2.27,16,98,2.98,3.15,.22,1.85,7.22,1.01,3.55,1045
1,14.1,2.16,2.3,18,105,2.95,3.32,.22,2.38,5.75,1.25,3.17,1510
1,14.12,1.48,2.32,16.8,95,2.2,2.43,.26,1.57,5,1.17,2.82,1280
1,13.75,1.73,2.41,16,89,2.6,2.76,.29,1.81,5.6,1.15,2.9,1320
1,14.75,1.73,2.39,11.4,91,3.1,3.69,.43,2.81,5.4,1.25,2.73,1150
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1,14.06,1.63,2.28,16,126,3,3.17,.24,2.1,5.65,1.09,3.71,780
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1 1 14.23 1.71 2.43 15.6 127 2.8 3.06 .28 2.29 5.64 1.04 3.92 1065
2 1 13.2 1.78 2.14 11.2 100 2.65 2.76 .26 1.28 4.38 1.05 3.4 1050
3 1 13.16 2.36 2.67 18.6 101 2.8 3.24 .3 2.81 5.68 1.03 3.17 1185
4 1 14.37 1.95 2.5 16.8 113 3.85 3.49 .24 2.18 7.8 .86 3.45 1480
5 1 13.24 2.59 2.87 21 118 2.8 2.69 .39 1.82 4.32 1.04 2.93 735
6 1 14.2 1.76 2.45 15.2 112 3.27 3.39 .34 1.97 6.75 1.05 2.85 1450
7 1 14.39 1.87 2.45 14.6 96 2.5 2.52 .3 1.98 5.25 1.02 3.58 1290
8 1 14.06 2.15 2.61 17.6 121 2.6 2.51 .31 1.25 5.05 1.06 3.58 1295
9 1 14.83 1.64 2.17 14 97 2.8 2.98 .29 1.98 5.2 1.08 2.85 1045
10 1 13.86 1.35 2.27 16 98 2.98 3.15 .22 1.85 7.22 1.01 3.55 1045
11 1 14.1 2.16 2.3 18 105 2.95 3.32 .22 2.38 5.75 1.25 3.17 1510
12 1 14.12 1.48 2.32 16.8 95 2.2 2.43 .26 1.57 5 1.17 2.82 1280
13 1 13.75 1.73 2.41 16 89 2.6 2.76 .29 1.81 5.6 1.15 2.9 1320
14 1 14.75 1.73 2.39 11.4 91 3.1 3.69 .43 2.81 5.4 1.25 2.73 1150
15 1 14.38 1.87 2.38 12 102 3.3 3.64 .29 2.96 7.5 1.2 3 1547
16 1 13.63 1.81 2.7 17.2 112 2.85 2.91 .3 1.46 7.3 1.28 2.88 1310
17 1 14.3 1.92 2.72 20 120 2.8 3.14 .33 1.97 6.2 1.07 2.65 1280
18 1 13.83 1.57 2.62 20 115 2.95 3.4 .4 1.72 6.6 1.13 2.57 1130
19 1 14.19 1.59 2.48 16.5 108 3.3 3.93 .32 1.86 8.7 1.23 2.82 1680
20 1 13.64 3.1 2.56 15.2 116 2.7 3.03 .17 1.66 5.1 .96 3.36 845
21 1 14.06 1.63 2.28 16 126 3 3.17 .24 2.1 5.65 1.09 3.71 780
22 1 12.93 3.8 2.65 18.6 102 2.41 2.41 .25 1.98 4.5 1.03 3.52 770
23 1 13.71 1.86 2.36 16.6 101 2.61 2.88 .27 1.69 3.8 1.11 4 1035
24 1 12.85 1.6 2.52 17.8 95 2.48 2.37 .26 1.46 3.93 1.09 3.63 1015
25 1 13.5 1.81 2.61 20 96 2.53 2.61 .28 1.66 3.52 1.12 3.82 845
26 1 13.05 2.05 3.22 25 124 2.63 2.68 .47 1.92 3.58 1.13 3.2 830
27 1 13.39 1.77 2.62 16.1 93 2.85 2.94 .34 1.45 4.8 .92 3.22 1195
28 1 13.3 1.72 2.14 17 94 2.4 2.19 .27 1.35 3.95 1.02 2.77 1285
29 1 13.87 1.9 2.8 19.4 107 2.95 2.97 .37 1.76 4.5 1.25 3.4 915
30 1 14.02 1.68 2.21 16 96 2.65 2.33 .26 1.98 4.7 1.04 3.59 1035
31 1 13.73 1.5 2.7 22.5 101 3 3.25 .29 2.38 5.7 1.19 2.71 1285
32 1 13.58 1.66 2.36 19.1 106 2.86 3.19 .22 1.95 6.9 1.09 2.88 1515
33 1 13.68 1.83 2.36 17.2 104 2.42 2.69 .42 1.97 3.84 1.23 2.87 990
34 1 13.76 1.53 2.7 19.5 132 2.95 2.74 .5 1.35 5.4 1.25 3 1235
35 1 13.51 1.8 2.65 19 110 2.35 2.53 .29 1.54 4.2 1.1 2.87 1095
36 1 13.48 1.81 2.41 20.5 100 2.7 2.98 .26 1.86 5.1 1.04 3.47 920
37 1 13.28 1.64 2.84 15.5 110 2.6 2.68 .34 1.36 4.6 1.09 2.78 880
38 1 13.05 1.65 2.55 18 98 2.45 2.43 .29 1.44 4.25 1.12 2.51 1105
39 1 13.07 1.5 2.1 15.5 98 2.4 2.64 .28 1.37 3.7 1.18 2.69 1020
40 1 14.22 3.99 2.51 13.2 128 3 3.04 .2 2.08 5.1 .89 3.53 760
41 1 13.56 1.71 2.31 16.2 117 3.15 3.29 .34 2.34 6.13 .95 3.38 795
42 1 13.41 3.84 2.12 18.8 90 2.45 2.68 .27 1.48 4.28 .91 3 1035
43 1 13.88 1.89 2.59 15 101 3.25 3.56 .17 1.7 5.43 .88 3.56 1095
44 1 13.24 3.98 2.29 17.5 103 2.64 2.63 .32 1.66 4.36 .82 3 680
45 1 13.05 1.77 2.1 17 107 3 3 .28 2.03 5.04 .88 3.35 885
46 1 14.21 4.04 2.44 18.9 111 2.85 2.65 .3 1.25 5.24 .87 3.33 1080
47 1 14.38 3.59 2.28 16 102 3.25 3.17 .27 2.19 4.9 1.04 3.44 1065
48 1 13.9 1.68 2.12 16 101 3.1 3.39 .21 2.14 6.1 .91 3.33 985
49 1 14.1 2.02 2.4 18.8 103 2.75 2.92 .32 2.38 6.2 1.07 2.75 1060
50 1 13.94 1.73 2.27 17.4 108 2.88 3.54 .32 2.08 8.90 1.12 3.1 1260
51 1 13.05 1.73 2.04 12.4 92 2.72 3.27 .17 2.91 7.2 1.12 2.91 1150
52 1 13.83 1.65 2.6 17.2 94 2.45 2.99 .22 2.29 5.6 1.24 3.37 1265
53 1 13.82 1.75 2.42 14 111 3.88 3.74 .32 1.87 7.05 1.01 3.26 1190
54 1 13.77 1.9 2.68 17.1 115 3 2.79 .39 1.68 6.3 1.13 2.93 1375
55 1 13.74 1.67 2.25 16.4 118 2.6 2.9 .21 1.62 5.85 .92 3.2 1060
56 1 13.56 1.73 2.46 20.5 116 2.96 2.78 .2 2.45 6.25 .98 3.03 1120
57 1 14.22 1.7 2.3 16.3 118 3.2 3 .26 2.03 6.38 .94 3.31 970
58 1 13.29 1.97 2.68 16.8 102 3 3.23 .31 1.66 6 1.07 2.84 1270
59 1 13.72 1.43 2.5 16.7 108 3.4 3.67 .19 2.04 6.8 .89 2.87 1285
60 2 12.37 .94 1.36 10.6 88 1.98 .57 .28 .42 1.95 1.05 1.82 520
61 2 12.33 1.1 2.28 16 101 2.05 1.09 .63 .41 3.27 1.25 1.67 680
62 2 12.64 1.36 2.02 16.8 100 2.02 1.41 .53 .62 5.75 .98 1.59 450
63 2 13.67 1.25 1.92 18 94 2.1 1.79 .32 .73 3.8 1.23 2.46 630
64 2 12.37 1.13 2.16 19 87 3.5 3.1 .19 1.87 4.45 1.22 2.87 420
65 2 12.17 1.45 2.53 19 104 1.89 1.75 .45 1.03 2.95 1.45 2.23 355
66 2 12.37 1.21 2.56 18.1 98 2.42 2.65 .37 2.08 4.6 1.19 2.3 678
67 2 13.11 1.01 1.7 15 78 2.98 3.18 .26 2.28 5.3 1.12 3.18 502
68 2 12.37 1.17 1.92 19.6 78 2.11 2 .27 1.04 4.68 1.12 3.48 510
69 2 13.34 .94 2.36 17 110 2.53 1.3 .55 .42 3.17 1.02 1.93 750
70 2 12.21 1.19 1.75 16.8 151 1.85 1.28 .14 2.5 2.85 1.28 3.07 718
71 2 12.29 1.61 2.21 20.4 103 1.1 1.02 .37 1.46 3.05 .906 1.82 870
72 2 13.86 1.51 2.67 25 86 2.95 2.86 .21 1.87 3.38 1.36 3.16 410
73 2 13.49 1.66 2.24 24 87 1.88 1.84 .27 1.03 3.74 .98 2.78 472
74 2 12.99 1.67 2.6 30 139 3.3 2.89 .21 1.96 3.35 1.31 3.5 985
75 2 11.96 1.09 2.3 21 101 3.38 2.14 .13 1.65 3.21 .99 3.13 886
76 2 11.66 1.88 1.92 16 97 1.61 1.57 .34 1.15 3.8 1.23 2.14 428
77 2 13.03 .9 1.71 16 86 1.95 2.03 .24 1.46 4.6 1.19 2.48 392
78 2 11.84 2.89 2.23 18 112 1.72 1.32 .43 .95 2.65 .96 2.52 500
79 2 12.33 .99 1.95 14.8 136 1.9 1.85 .35 2.76 3.4 1.06 2.31 750
80 2 12.7 3.87 2.4 23 101 2.83 2.55 .43 1.95 2.57 1.19 3.13 463
81 2 12 .92 2 19 86 2.42 2.26 .3 1.43 2.5 1.38 3.12 278
82 2 12.72 1.81 2.2 18.8 86 2.2 2.53 .26 1.77 3.9 1.16 3.14 714
83 2 12.08 1.13 2.51 24 78 2 1.58 .4 1.4 2.2 1.31 2.72 630
84 2 13.05 3.86 2.32 22.5 85 1.65 1.59 .61 1.62 4.8 .84 2.01 515
85 2 11.84 .89 2.58 18 94 2.2 2.21 .22 2.35 3.05 .79 3.08 520
86 2 12.67 .98 2.24 18 99 2.2 1.94 .3 1.46 2.62 1.23 3.16 450
87 2 12.16 1.61 2.31 22.8 90 1.78 1.69 .43 1.56 2.45 1.33 2.26 495
88 2 11.65 1.67 2.62 26 88 1.92 1.61 .4 1.34 2.6 1.36 3.21 562
89 2 11.64 2.06 2.46 21.6 84 1.95 1.69 .48 1.35 2.8 1 2.75 680
90 2 12.08 1.33 2.3 23.6 70 2.2 1.59 .42 1.38 1.74 1.07 3.21 625
91 2 12.08 1.83 2.32 18.5 81 1.6 1.5 .52 1.64 2.4 1.08 2.27 480
92 2 12 1.51 2.42 22 86 1.45 1.25 .5 1.63 3.6 1.05 2.65 450
93 2 12.69 1.53 2.26 20.7 80 1.38 1.46 .58 1.62 3.05 .96 2.06 495
94 2 12.29 2.83 2.22 18 88 2.45 2.25 .25 1.99 2.15 1.15 3.3 290
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21.252 -555.640
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6.2,29
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import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
data = pd.read_csv('fires_thefts.csv', names = ['fires', 'thefts'])
print(data)
x = data[['fires']].to_numpy().flatten()
y = data[['thefts']].to_numpy().flatten()
def gradient_descent(h, cost_fun, theta, x, y, alpha, eps, max_steps = 1000000):
current_cost = cost_fun(h, theta, x, y)
log = [[current_cost, theta]]
m = len(y)
steps_counter = 0
while True and steps_counter < max_steps:
steps_counter += 1
new_theta = [
theta[0] - alpha/float(m) * sum(h(theta, x[i]) - y[i]
for i in range(m)),
theta[1] - alpha/float(m) * sum((h(theta, x[i]) - y[i]) * x[i]
for i in range(m))]
theta = new_theta
prev_cost = current_cost
current_cost = cost_fun(h, theta, x, y)
if abs(prev_cost - current_cost) <= eps:
break
log.append([current_cost, theta])
return theta, log
def J(h, theta, x, y):
m = len(y)
return 1.0 / (2 * m) * sum((h(theta, x[i]) - y[i])**2 for i in range(m))
def h(theta, x):
return theta[0] + theta[1] * x
def mse(expected, predicted):
m = len(expected)
if len(predicted) != m:
raise Exception('Wektory mają różne długości!')
return 1.0 / (2 * m) * sum((expected[i] - predicted[i])**2 for i in range(m))
best_theta, log = gradient_descent(h, J, [0.0, 0.0], x, y, alpha=0.001, eps=0.0000001, max_steps = 1000)
predicted_50 = h(best_theta, 50)
predicted_100 = h(best_theta, 100)
predicted_200 = h(best_theta, 200)
print(f'Predicted amount of thefts for 50 fires: {predicted_50}')
print(f'Predicted amount of thefts for 100 fires: {predicted_100}')
print(f'Predicted amount of thefts for 200 fires: {predicted_200}')
best_theta_01, log_01 = gradient_descent(h, J, [0.0, 0.0], x, y, alpha = 0.1, eps = 0.0000001, max_steps = 1000)
best_theta_001, log_001 = gradient_descent(h, J, [0.0, 0.0], x, y, alpha = 0.01, eps = 0.0000001, max_steps = 1000)
best_theta_0001, log_0001 = gradient_descent(h, J, [0.0, 0.0], x, y, alpha = 0.001, eps = 0.0000001, max_steps = 1000)
steps_range = np.arange(0, 200, 1)
y_01, y_001, y_0001 = [], [], []
for step in steps_range:
y_01.append(log_01[step][0])
y_001.append(log_001[step][0])
y_0001.append(log_0001[step][0])
fig = plt.figure(figsize=(8, 7))
ax = fig.add_subplot(111)
ax.plot(steps_range, y_01, label='alpha = 0.1')
ax.plot(steps_range, y_001, label='alpha = 0.01')
ax.plot(steps_range, y_0001, label='alpha = 0.001')
ax.legend(loc='best')
ax.set_xlabel('krok')
ax.set_ylabel(r'$J(\theta)$')
# plt.ylim([0, 800])
plt.show()

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sl,sw,pl,pw,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
5.6,2.5,3.9,1.1,Iris-versicolor
6.3,3.3,4.7,1.6,Iris-versicolor
5.1,3.4,1.5,0.2,Iris-setosa
6.0,2.9,4.5,1.5,Iris-versicolor
5.3,3.7,1.5,0.2,Iris-setosa
5.6,2.9,3.6,1.3,Iris-versicolor
5.5,2.5,4.0,1.3,Iris-versicolor
5.5,2.4,3.7,1.0,Iris-versicolor
4.4,3.0,1.3,0.2,Iris-setosa
6.6,3.0,4.4,1.4,Iris-versicolor
7.9,3.8,6.4,2.0,Iris-virginica
5.7,2.8,4.1,1.3,Iris-versicolor
5.8,2.7,4.1,1.0,Iris-versicolor
6.5,2.8,4.6,1.5,Iris-versicolor
6.1,2.8,4.7,1.2,Iris-versicolor
5.1,3.8,1.9,0.4,Iris-setosa
5.0,3.4,1.6,0.4,Iris-setosa
5.5,2.6,4.4,1.2,Iris-versicolor
5.0,3.4,1.5,0.2,Iris-setosa
6.8,2.8,4.8,1.4,Iris-versicolor
6.9,3.1,4.9,1.5,Iris-versicolor
6.1,2.9,4.7,1.4,Iris-versicolor
5.1,3.8,1.6,0.2,Iris-setosa
6.4,3.2,5.3,2.3,Iris-virginica
6.4,2.7,5.3,1.9,Iris-virginica
5.7,2.8,4.5,1.3,Iris-versicolor
5.8,2.6,4.0,1.2,Iris-versicolor
4.7,3.2,1.6,0.2,Iris-setosa
5.1,3.3,1.7,0.5,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
6.3,3.4,5.6,2.4,Iris-virginica
5.1,3.8,1.5,0.3,Iris-setosa
7.0,3.2,4.7,1.4,Iris-versicolor
5.4,3.0,4.5,1.5,Iris-versicolor
6.0,2.2,4.0,1.0,Iris-versicolor
6.0,3.0,4.8,1.8,Iris-virginica
6.2,2.9,4.3,1.3,Iris-versicolor
5.6,3.0,4.1,1.3,Iris-versicolor
4.9,3.0,1.4,0.2,Iris-setosa
5.0,2.3,3.3,1.0,Iris-versicolor
6.3,2.5,5.0,1.9,Iris-virginica
4.8,3.4,1.6,0.2,Iris-setosa
5.9,3.0,4.2,1.5,Iris-versicolor
4.6,3.6,1.0,0.2,Iris-setosa
5.0,3.5,1.6,0.6,Iris-setosa
5.7,4.4,1.5,0.4,Iris-setosa
5.0,3.0,1.6,0.2,Iris-setosa
5.6,3.0,4.5,1.5,Iris-versicolor
6.3,2.8,5.1,1.5,Iris-virginica
5.2,2.7,3.9,1.4,Iris-versicolor
5.9,3.2,4.8,1.8,Iris-versicolor
7.7,3.0,6.1,2.3,Iris-virginica
6.2,3.4,5.4,2.3,Iris-virginica
6.4,2.9,4.3,1.3,Iris-versicolor
6.5,3.0,5.5,1.8,Iris-virginica
5.8,2.7,5.1,1.9,Iris-virginica
6.9,3.2,5.7,2.3,Iris-virginica
6.4,2.8,5.6,2.2,Iris-virginica
4.7,3.2,1.3,0.2,Iris-setosa
5.5,2.4,3.8,1.1,Iris-versicolor
5.4,3.4,1.5,0.4,Iris-setosa
7.2,3.6,6.1,2.5,Iris-virginica
6.7,2.5,5.8,1.8,Iris-virginica
6.1,3.0,4.6,1.4,Iris-versicolor
6.0,3.4,4.5,1.6,Iris-versicolor
6.3,2.7,4.9,1.8,Iris-virginica
6.9,3.1,5.1,2.3,Iris-virginica
5.5,3.5,1.3,0.2,Iris-setosa
6.7,3.0,5.2,2.3,Iris-virginica
4.6,3.1,1.5,0.2,Iris-setosa
5.8,2.7,5.1,1.9,Iris-virginica
6.4,3.1,5.5,1.8,Iris-virginica
7.3,2.9,6.3,1.8,Iris-virginica
4.8,3.0,1.4,0.3,Iris-setosa
7.1,3.0,5.9,2.1,Iris-virginica
5.9,3.0,5.1,1.8,Iris-virginica
6.1,2.6,5.6,1.4,Iris-virginica
5.4,3.9,1.7,0.4,Iris-setosa
6.4,3.2,4.5,1.5,Iris-versicolor
5.1,2.5,3.0,1.1,Iris-versicolor
6.3,2.9,5.6,1.8,Iris-virginica
7.2,3.2,6.0,1.8,Iris-virginica
5.4,3.4,1.7,0.2,Iris-setosa
4.6,3.2,1.4,0.2,Iris-setosa
6.1,2.8,4.0,1.3,Iris-versicolor
7.7,3.8,6.7,2.2,Iris-virginica
5.7,2.9,4.2,1.3,Iris-versicolor
5.1,3.5,1.4,0.2,Iris-setosa
4.9,3.1,1.5,0.1,Iris-setosa
6.5,3.0,5.2,2.0,Iris-virginica
4.9,3.1,1.5,0.1,Iris-setosa
6.3,2.3,4.4,1.3,Iris-versicolor
6.2,2.2,4.5,1.5,Iris-versicolor
5.7,3.8,1.7,0.3,Iris-setosa
6.4,2.8,5.6,2.1,Iris-virginica
4.9,2.4,3.3,1.0,Iris-versicolor
5.7,2.5,5.0,2.0,Iris-virginica
5.5,4.2,1.4,0.2,Iris-setosa
6.7,3.0,5.0,1.7,Iris-versicolor
5.0,3.3,1.4,0.2,Iris-setosa
6.3,2.5,4.9,1.5,Iris-versicolor
5.4,3.7,1.5,0.2,Iris-setosa
7.7,2.6,6.9,2.3,Iris-virginica
5.7,3.0,4.2,1.2,Iris-versicolor
7.6,3.0,6.6,2.1,Iris-virginica
4.8,3.1,1.6,0.2,Iris-setosa
5.6,2.8,4.9,2.0,Iris-virginica
4.5,2.3,1.3,0.3,Iris-setosa
6.8,3.2,5.9,2.3,Iris-virginica
6.3,3.3,6.0,2.5,Iris-virginica
4.6,3.4,1.4,0.3,Iris-setosa
5.8,2.7,3.9,1.2,Iris-versicolor
5.5,2.3,4.0,1.3,Iris-versicolor
5.2,4.1,1.5,0.1,Iris-setosa
6.6,2.9,4.6,1.3,Iris-versicolor
4.3,3.0,1.1,0.1,Iris-setosa
6.8,3.0,5.5,2.1,Iris-virginica
5.8,4.0,1.2,0.2,Iris-setosa
5.1,3.5,1.4,0.3,Iris-setosa
6.5,3.0,5.8,2.2,Iris-virginica
6.9,3.1,5.4,2.1,Iris-virginica
6.7,3.3,5.7,2.1,Iris-virginica
1 sl sw pl pw Gatunek
2 5.2 3.4 1.4 0.2 Iris-setosa
3 5.1 3.7 1.5 0.4 Iris-setosa
4 6.7 3.1 5.6 2.4 Iris-virginica
5 6.5 3.2 5.1 2.0 Iris-virginica
6 4.9 2.5 4.5 1.7 Iris-virginica
7 6.0 2.7 5.1 1.6 Iris-versicolor
8 5.7 2.6 3.5 1.0 Iris-versicolor
9 5.0 2.0 3.5 1.0 Iris-versicolor
10 5.2 3.5 1.5 0.2 Iris-setosa
11 4.8 3.0 1.4 0.1 Iris-setosa
12 6.7 3.3 5.7 2.5 Iris-virginica
13 6.1 3.0 4.9 1.8 Iris-virginica
14 4.8 3.4 1.9 0.2 Iris-setosa
15 5.8 2.8 5.1 2.4 Iris-virginica
16 4.4 2.9 1.4 0.2 Iris-setosa
17 7.2 3.0 5.8 1.6 Iris-virginica
18 4.4 3.2 1.3 0.2 Iris-setosa
19 5.0 3.5 1.3 0.3 Iris-setosa
20 5.4 3.9 1.3 0.4 Iris-setosa
21 7.7 2.8 6.7 2.0 Iris-virginica
22 5.0 3.6 1.4 0.2 Iris-setosa
23 6.2 2.8 4.8 1.8 Iris-virginica
24 6.0 2.2 5.0 1.5 Iris-virginica
25 7.4 2.8 6.1 1.9 Iris-virginica
26 5.0 3.2 1.2 0.2 Iris-setosa
27 6.7 3.1 4.4 1.4 Iris-versicolor
28 6.7 3.1 4.7 1.5 Iris-versicolor
29 5.6 2.7 4.2 1.3 Iris-versicolor
30 5.6 2.5 3.9 1.1 Iris-versicolor
31 6.3 3.3 4.7 1.6 Iris-versicolor
32 5.1 3.4 1.5 0.2 Iris-setosa
33 6.0 2.9 4.5 1.5 Iris-versicolor
34 5.3 3.7 1.5 0.2 Iris-setosa
35 5.6 2.9 3.6 1.3 Iris-versicolor
36 5.5 2.5 4.0 1.3 Iris-versicolor
37 5.5 2.4 3.7 1.0 Iris-versicolor
38 4.4 3.0 1.3 0.2 Iris-setosa
39 6.6 3.0 4.4 1.4 Iris-versicolor
40 7.9 3.8 6.4 2.0 Iris-virginica
41 5.7 2.8 4.1 1.3 Iris-versicolor
42 5.8 2.7 4.1 1.0 Iris-versicolor
43 6.5 2.8 4.6 1.5 Iris-versicolor
44 6.1 2.8 4.7 1.2 Iris-versicolor
45 5.1 3.8 1.9 0.4 Iris-setosa
46 5.0 3.4 1.6 0.4 Iris-setosa
47 5.5 2.6 4.4 1.2 Iris-versicolor
48 5.0 3.4 1.5 0.2 Iris-setosa
49 6.8 2.8 4.8 1.4 Iris-versicolor
50 6.9 3.1 4.9 1.5 Iris-versicolor
51 6.1 2.9 4.7 1.4 Iris-versicolor
52 5.1 3.8 1.6 0.2 Iris-setosa
53 6.4 3.2 5.3 2.3 Iris-virginica
54 6.4 2.7 5.3 1.9 Iris-virginica
55 5.7 2.8 4.5 1.3 Iris-versicolor
56 5.8 2.6 4.0 1.2 Iris-versicolor
57 4.7 3.2 1.6 0.2 Iris-setosa
58 5.1 3.3 1.7 0.5 Iris-setosa
59 4.9 3.1 1.5 0.1 Iris-setosa
60 6.3 3.4 5.6 2.4 Iris-virginica
61 5.1 3.8 1.5 0.3 Iris-setosa
62 7.0 3.2 4.7 1.4 Iris-versicolor
63 5.4 3.0 4.5 1.5 Iris-versicolor
64 6.0 2.2 4.0 1.0 Iris-versicolor
65 6.0 3.0 4.8 1.8 Iris-virginica
66 6.2 2.9 4.3 1.3 Iris-versicolor
67 5.6 3.0 4.1 1.3 Iris-versicolor
68 4.9 3.0 1.4 0.2 Iris-setosa
69 5.0 2.3 3.3 1.0 Iris-versicolor
70 6.3 2.5 5.0 1.9 Iris-virginica
71 4.8 3.4 1.6 0.2 Iris-setosa
72 5.9 3.0 4.2 1.5 Iris-versicolor
73 4.6 3.6 1.0 0.2 Iris-setosa
74 5.0 3.5 1.6 0.6 Iris-setosa
75 5.7 4.4 1.5 0.4 Iris-setosa
76 5.0 3.0 1.6 0.2 Iris-setosa
77 5.6 3.0 4.5 1.5 Iris-versicolor
78 6.3 2.8 5.1 1.5 Iris-virginica
79 5.2 2.7 3.9 1.4 Iris-versicolor
80 5.9 3.2 4.8 1.8 Iris-versicolor
81 7.7 3.0 6.1 2.3 Iris-virginica
82 6.2 3.4 5.4 2.3 Iris-virginica
83 6.4 2.9 4.3 1.3 Iris-versicolor
84 6.5 3.0 5.5 1.8 Iris-virginica
85 5.8 2.7 5.1 1.9 Iris-virginica
86 6.9 3.2 5.7 2.3 Iris-virginica
87 6.4 2.8 5.6 2.2 Iris-virginica
88 4.7 3.2 1.3 0.2 Iris-setosa
89 5.5 2.4 3.8 1.1 Iris-versicolor
90 5.4 3.4 1.5 0.4 Iris-setosa
91 7.2 3.6 6.1 2.5 Iris-virginica
92 6.7 2.5 5.8 1.8 Iris-virginica
93 6.1 3.0 4.6 1.4 Iris-versicolor
94 6.0 3.4 4.5 1.6 Iris-versicolor
95 6.3 2.7 4.9 1.8 Iris-virginica
96 6.9 3.1 5.1 2.3 Iris-virginica
97 5.5 3.5 1.3 0.2 Iris-setosa
98 6.7 3.0 5.2 2.3 Iris-virginica
99 4.6 3.1 1.5 0.2 Iris-setosa
100 5.8 2.7 5.1 1.9 Iris-virginica
101 6.4 3.1 5.5 1.8 Iris-virginica
102 7.3 2.9 6.3 1.8 Iris-virginica
103 4.8 3.0 1.4 0.3 Iris-setosa
104 7.1 3.0 5.9 2.1 Iris-virginica
105 5.9 3.0 5.1 1.8 Iris-virginica
106 6.1 2.6 5.6 1.4 Iris-virginica
107 5.4 3.9 1.7 0.4 Iris-setosa
108 6.4 3.2 4.5 1.5 Iris-versicolor
109 5.1 2.5 3.0 1.1 Iris-versicolor
110 6.3 2.9 5.6 1.8 Iris-virginica
111 7.2 3.2 6.0 1.8 Iris-virginica
112 5.4 3.4 1.7 0.2 Iris-setosa
113 4.6 3.2 1.4 0.2 Iris-setosa
114 6.1 2.8 4.0 1.3 Iris-versicolor
115 7.7 3.8 6.7 2.2 Iris-virginica
116 5.7 2.9 4.2 1.3 Iris-versicolor
117 5.1 3.5 1.4 0.2 Iris-setosa
118 4.9 3.1 1.5 0.1 Iris-setosa
119 6.5 3.0 5.2 2.0 Iris-virginica
120 4.9 3.1 1.5 0.1 Iris-setosa
121 6.3 2.3 4.4 1.3 Iris-versicolor
122 6.2 2.2 4.5 1.5 Iris-versicolor
123 5.7 3.8 1.7 0.3 Iris-setosa
124 6.4 2.8 5.6 2.1 Iris-virginica
125 4.9 2.4 3.3 1.0 Iris-versicolor
126 5.7 2.5 5.0 2.0 Iris-virginica
127 5.5 4.2 1.4 0.2 Iris-setosa
128 6.7 3.0 5.0 1.7 Iris-versicolor
129 5.0 3.3 1.4 0.2 Iris-setosa
130 6.3 2.5 4.9 1.5 Iris-versicolor
131 5.4 3.7 1.5 0.2 Iris-setosa
132 7.7 2.6 6.9 2.3 Iris-virginica
133 5.7 3.0 4.2 1.2 Iris-versicolor
134 7.6 3.0 6.6 2.1 Iris-virginica
135 4.8 3.1 1.6 0.2 Iris-setosa
136 5.6 2.8 4.9 2.0 Iris-virginica
137 4.5 2.3 1.3 0.3 Iris-setosa
138 6.8 3.2 5.9 2.3 Iris-virginica
139 6.3 3.3 6.0 2.5 Iris-virginica
140 4.6 3.4 1.4 0.3 Iris-setosa
141 5.8 2.7 3.9 1.2 Iris-versicolor
142 5.5 2.3 4.0 1.3 Iris-versicolor
143 5.2 4.1 1.5 0.1 Iris-setosa
144 6.6 2.9 4.6 1.3 Iris-versicolor
145 4.3 3.0 1.1 0.1 Iris-setosa
146 6.8 3.0 5.5 2.1 Iris-virginica
147 5.8 4.0 1.2 0.2 Iris-setosa
148 5.1 3.5 1.4 0.3 Iris-setosa
149 6.5 3.0 5.8 2.2 Iris-virginica
150 6.9 3.1 5.4 2.1 Iris-virginica
151 6.7 3.3 5.7 2.1 Iris-virginica