# Lecture21HO - 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) Supervised learning Training: Fnd h( x ) Given a training set D train of items ( x i , y i = f( x i )) , return a function h( x ) which approximates f( x ) Testing: how well does h( x ) generalize? Given a test set D test of items x i that is disjoint from D train , evaluate how close h( x ) is to f( x ) . (classiFcation) accuracy: pctg. of x i D test : h( x i ) = f( x i ) 4 CS440/ECE448: Intro AI train test

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N -fold cross-validation A better indication of how well h(x) generalizes: Split data into N equal-sized parts, Run and evaluate N experiments Report average accuracy, variance, etc. 5 CS440/ECE448: Intro AI 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) 6 CS440/ECE448: Intro AI C A1 A2 An An example Can you train a Naïve Bayes classiFer to predict whether the customer wants sugar or not? What is P(coffee | sugar)? 7 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 Questions that came up in class… What are the independence assumptions that Naïve Bayes makes? Are drink and milk independent R.V.s? Are they conditionally independent, given sugar? What happens when your Bayes Net makes independence assumptions that are incorrect? 8 CS440/ECE448: Intro AI
Decision trees Decision trees In this example, the attributes (drink; milk?) are not conditionally independent given the class ( ʻ sugar ʼ ) 10 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

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Lecture21HO - CS440/ECE448 Intro to Articial Intelligence...

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