# Lecture20 - CS440/ECE448: Intro to Articial Intelligence!...

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Lecture 20 More on learning graphical models Prof. Julia Hockenmaier juliahmr@illinois.edu http://cs.illinois.edu/fa11/cs440 CS440/ECE448: Intro to ArtiFcial Intelligence

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Bayes Nets A Bayes Net defnes a joint distribution P(X 1 …X n ) over a set oF random variables X 1 …X n Using the chain ru le, we can Factor P(X 1 …X n ) into a product oF n conditional distributions : P(X 1 …X n ) = ! j P(X i | X 1 …X i-1 ). A Bayes Net makes a number oF (conditional) independence assumptions: P(X 1 …X n ) = def ! j P(X i | Parents(X i ) ˧ {X 1… X i-1 })
Learning Bayes Nets Parameter estimation: Given some data D over a set of random variables X and a Bayes Net (with empty CPTs) estimate the parameters (= Fll in the CPTs) of the Bayes Net . Structure learning: Given some data D over a set of random variables X , Fnd a Bayes Net (deFne its CPTs) and estimate its parameters. (This is much harder… we won ʼ t deal with it here)

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Bayes Rule P(h): prior probability of hypothesis P(h | D) : posterior probability
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## Lecture20 - CS440/ECE448: Intro to Articial Intelligence!...

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