# Lecture26HO - Lecture 26 A bit about learning theory Prof...

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Unformatted text preview: Lecture 26: A bit about learning theory Prof. Julia Hockenmaier [email protected] http://cs.illinois.edu/fa11/cs440 CS440/ECE448: Intro to ArtiFcial Intelligence Monday, May 2 , 4 pm in 1404 Siebel Center Natural Language Applications Across Genres: From News to Novels Prof. Kathleen McKeown, Columbia University Monday, May 2 , 6 pm in 2405 Siebel Center Attending Graduate School: A panel discussion Tuesday, May 3 , 10 am 2405 Siebel Center Machine Learning - Modern Times Dr Corinna Cortes (Head of Google Research, NY) Binary classifcation: training Input: {( x i, y i )} with (x 1…. x d ) ˥ R d y i ˥ {+1, -1} Task: ¡ind weights w = (w w 1…. w d ) ˥ R d+1 that deFne f( x ) = wx 4 CS440/ECE448: Intro AI x 1 x 2 + + + + + + + + + x x x x x x x x x x Decision boundary f( x ) = 0 Boolean XOR XOR is not linearly separable 5 CS440/ECE448: Intro AI 0 1 x 1 x 2 1 0 From perceptrons to neural networks We can think of a single perceptron as one neuron 6 CS440/ECE448: Intro AI Output Σ Input Links Activation Function Input Function Output Links a 0 = 1 a j = g ( in j ) a j g in j w i,j w ,j Bias Weight a i Artifcial Neural Networks: Multi-layer perceptrons … ! " # … ! " # … ! " # ! " # … 7 From perceptrons to neural nets A neural net consists of nodes connected by directed links. Each node has an activation a i Links a ij propagate the activation a i from i to j. Each link has a weight w ij that determines the strength and sign of the connection 8 CS440/ECE448: Intro AI w 3,5 3,6 w 4,5 w 4,6 w 5 6 w 1,3 1,4 w 2,3 w 2,4 w 1 2 3 4 w 1,3 1,4 w 2,3 w 2,4 w 1 2 3 4 (b) (a) From perceptrons to neural networks Each unit computes a weighted sum of its inputs: in j = !...
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Lecture26HO - Lecture 26 A bit about learning theory Prof...

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