# Lecture22HO - CS440/ECE448 Intro to Articial Intelligence...

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Lecture 21: Classifcation; Decision Trees Prof. Julia Hockenmaier http://cs.illinois.edu/fa11/cs440 CS440/ECE448: Intro to ArtiFcial Intelligence Supervised learning: classifcation Supervised learning Given a set D of N items x i , each paired with an output value y i = f( x i ) , discover a function h( x ) which approximates f( x ) D = {( x 1 , y 1 ),… ( x N , y N )} Typically, the input values x are (real-valued or boolean) vectors : x i ˥ R n or x i {0,1} n The output values y are either boolean (binary classifcation) , elements of a Fnite set (multiclass classifcation) , or real (regression) The Naïve Bayes Classifer Each item has a number of attributes A 1 =a 1 ,…,A n =a n We predict the class c based on c = argmax c ! i P(A i = a i | C=c) P(C=c) 4 CS440/ECE448: Intro AI C A1 A2 An

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An example Can you train a Naïve Bayes classifer to predict whether the customer wants sugar or not? What is P(coFFee | sugar)? 5 CS440/ECE448: Intro AI x1 x2 Y A1: drink A2: milk? C: sugar? coFFee no yes coFFee yes no tea yes yes tea no no Decision trees Decision trees In this example, the attributes (drink; milk?) are not conditionally independent given the class ( ʻ sugar ʼ ) 7 CS440/ECE448: Intro AI drink? milk? milk? coFFee tea yes no no sugar sugar yes no sugar no sugar What is a decision tree? Test 2 Test 6 Test 5 Test 3 Test 4 V11 V22 V21 V12 V13 Label 2 Label 1 Label 1 test 1
Suppose I like circles that are red (I might not be aware of the rule) Features: Owner: John, Mary, Sam Size: Large, Small Shape : Triangle, Circle, Square Texture: Rough, Smooth Color: Blue, Red, Green, Yellow, Taupe Shape Triangle Circle Square Blue Red Green Yellow Taupe Color + - - - - - - ! x [Like(x) " (Circle(x) # Red(x))] Suppose I like circles that are red and triangles that are smooth Shape Triangle Circle Square Blue Red Green Yellow Taupe Color + - - - - - - ! x [Like(x) " ((Circle(x) # Red(x) v (Triangle(x) # Smooth(x))] texture smooth rough + Expressiveness of decision trees Consider binary classifcation (y= true,false ) where the items have Boolean attributes. In the decision tree, each

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Lecture22HO - CS440/ECE448 Intro to Articial Intelligence...

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