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

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Lecture 20 More on learning graphical models Prof. Julia Hockenmaier [email protected] http://cs.illinois.edu/fa11/cs440 CS440/ECE448: Intro to Artificial Intelligence

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Bayes Nets A Bayes Net defines 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 (= fill in the CPTs) of the Bayes Net . Structure learning: Given some data D over a set of random variables X , find a Bayes Net (define 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 of hypothesis.
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