Materiały na podstawie ZUMZ'19

w1/data01.csv

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w2/data_company.csv

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w2/ex2data2.txt

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w2/iris.csv

@@ -0,0 +1,151 @@
+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

w2/polynomial_logistic.tsv

@@ -0,0 +1,100 @@
+1	0.25777005758108174	0.601012316037165
+1	0.3659669567447452	-0.11214686303429633
+0	0.49453050141627375	0.47110655546911206
+0	0.7029060372914113	-0.9225798301680093
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+0	0.8793946243263941	-0.11408014657778076
+0	-0.3311850002119068	0.8444766749977881
+0	-0.5435170087333634	0.8851383010436487
+0	0.9197924083397226	0.41607011737177735
+0	0.28011742147804797	0.6143115673056148
+0	0.9475436344725683	-0.7830731144606005
+0	0.4904989452188586	0.649356142549592
+0	-0.865983500565505	0.9896361556274065
+0	-0.8579184997717257	0.3062253122060574
+0	0.08082005095746103	-0.7736760810964189
+0	-0.3363842450225085	-0.8802992880290186
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w3/bayes_nasty.tsv

@@ -0,0 +1,100 @@
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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])

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
+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

w3/tennis.tsv

@@ -0,0 +1,15 @@
+Day	Outlook	Humidity	Wind	Play
+1	Sunny	High	Weak	No
+2	Sunny	High	Strong	No
+3	Overcast	High	Weak	Yes
+4	Rain	High	Weak	Yes
+5	Rain	Normal	Weak	Yes
+6	Rain	Normal	Strong	No
+7	Overcast	Normal	Strong	Yes
+8	Sunny	High	Weak	No
+9	Sunny	Normal	Weak	Yes
+10	Rain	Normal	Weak	Yes
+11	Sunny	Normal	Strong	Yes
+12	Overcast	High	Strong	Yes
+13	Overcast	Normal	Weak	Yes
+14	Rain	High	Strong	No

w3/zumz3b.ipynb

@@ -0,0 +1,847 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "slideshow": {
+     "slide_type": "slide"
+    }
+   },
+   "source": [
+    "## Uczenie maszynowe UMZ 2017/2018\n",
+    "# 3. 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": [
+       "<div>\n",
+       "<style>\n",
+       "    .dataframe thead tr:only-child th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: left;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>Day</th>\n",
+       "      <th>Outlook</th>\n",
+       "      <th>Humidity</th>\n",
+       "      <th>Wind</th>\n",
+       "      <th>Play</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>1</td>\n",
+       "      <td>Sunny</td>\n",
+       "      <td>High</td>\n",
+       "      <td>Weak</td>\n",
+       "      <td>No</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>2</td>\n",
+       "      <td>Sunny</td>\n",
+       "      <td>High</td>\n",
+       "      <td>Strong</td>\n",
+       "      <td>No</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>3</td>\n",
+       "      <td>Overcast</td>\n",
+       "      <td>High</td>\n",
+       "      <td>Weak</td>\n",
+       "      <td>Yes</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>4</td>\n",
+       "      <td>Rain</td>\n",
+       "      <td>High</td>\n",
+       "      <td>Weak</td>\n",
+       "      <td>Yes</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>5</td>\n",
+       "      <td>Rain</td>\n",
+       "      <td>Normal</td>\n",
+       "      <td>Weak</td>\n",
+       "      <td>Yes</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>5</th>\n",
+       "      <td>6</td>\n",
+       "      <td>Rain</td>\n",
+       "      <td>Normal</td>\n",
+       "      <td>Strong</td>\n",
+       "      <td>No</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>6</th>\n",
+       "      <td>7</td>\n",
+       "      <td>Overcast</td>\n",
+       "      <td>Normal</td>\n",
+       "      <td>Strong</td>\n",
+       "      <td>Yes</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>7</th>\n",
+       "      <td>8</td>\n",
+       "      <td>Sunny</td>\n",
+       "      <td>High</td>\n",
+       "      <td>Weak</td>\n",
+       "      <td>No</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>8</th>\n",
+       "      <td>9</td>\n",
+       "      <td>Sunny</td>\n",
+       "      <td>Normal</td>\n",
+       "      <td>Weak</td>\n",
+       "      <td>Yes</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>9</th>\n",
+       "      <td>10</td>\n",
+       "      <td>Rain</td>\n",
+       "      <td>Normal</td>\n",
+       "      <td>Weak</td>\n",
+       "      <td>Yes</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>10</th>\n",
+       "      <td>11</td>\n",
+       "      <td>Sunny</td>\n",
+       "      <td>Normal</td>\n",
+       "      <td>Strong</td>\n",
+       "      <td>Yes</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>11</th>\n",
+       "      <td>12</td>\n",
+       "      <td>Overcast</td>\n",
+       "      <td>High</td>\n",
+       "      <td>Strong</td>\n",
+       "      <td>Yes</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>12</th>\n",
+       "      <td>13</td>\n",
+       "      <td>Overcast</td>\n",
+       "      <td>Normal</td>\n",
+       "      <td>Weak</td>\n",
+       "      <td>Yes</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>13</th>\n",
+       "      <td>14</td>\n",
+       "      <td>Rain</td>\n",
+       "      <td>High</td>\n",
+       "      <td>Strong</td>\n",
+       "      <td>No</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "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
+}

w4/classification.tsv

@@ -0,0 +1,20 @@
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+1	0.7967711966832445	-0.4352501064041614
+1	0.8053812216632301	0.1203107620499666

w4/create_polynomial_logistic.py

@@ -0,0 +1,26 @@
+#!/usr/bin/python3
+# -*- coding:utf-8 -*-
+
+
+import csv
+import math
+import random
+import sys
+
+
+def create_polynomial_logistic_data(filename):
+    with open(filename, 'w') as f:
+        writer = csv.writer(
+            f, delimiter=('\t' if filename.endswith('.tsv') else ','))
+        for i in range(50):
+            x = random.uniform(-1.0, 1.0)
+            y = random.uniform(-1.0, 1.0)
+            p = math.sqrt(x*x + y*y)
+            for i in range(1):
+                p = -2 * p**3 + 3 * p**2
+            v = 1 if random.random() > p else 0
+            writer.writerow([v, x, y])
+
+
+if __name__ == '__main__':
+    create_polynomial_logistic_data(sys.argv[1])

w4/data.tsv

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+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

w5/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
+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