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Lecture25 - CS440/ECE448 Intro to Articial Intelligence...

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Lecture 25: Perceptrons II Prof. Julia Hockenmaier [email protected] http://cs.illinois.edu/fa11/cs440 CS440/ECE448: Intro to Artificial Intelligence
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Binary classification Input: x = (x 1…. x d ) R d Output: return the class predicted by h w ( x ) h w ( x ): if f( x )= wx > 0 return y = 1, else return y = 0 2 CS440/ECE448: Intro AI x 1 x 2 + + + + + + + + + x x x x x x x x x x Decision boundary f( x ) = 0
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Binary classification: training Input: {( x i, y i )} with (x 1…. x d ) R d y i {+1, -1} Task: Find weights w = (w 0 w 1…. w d ) R d+1 that define f( x ) = wx 3 CS440/ECE448: Intro AI x 1 x 2 + + + + + + + + + x x x x x x x x x x Decision boundary f( x ) = 0
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Perceptron algorithm Given training data {( x 1 , y 1 ),…,( x j , y j ),…,( x N , y N )} Start with initial weight vector w Online update: Update w for each ( x j , y j ) w i := w i + α (y j - h w ( x j ))x i j Batch update: Go through entire data set before updating w Δ w i = j ( α (y j - h w ( x ))x i j ) w i := w i + Δ w i The learning rate α decays over time 4 CS440/ECE448: Intro AI
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Perceptron Example Space Input: a vector of n components If input is a vector of Booleans
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