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SumProd

SumProd - Sum-Product Algorithm CSci 5512 Artificial...

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Sum-Product Algorithm CSci 5512: Artificial Intelligence II

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Factor Graphs Many problems deal with global function of many variables Global function “factors” into product of local functions E ff٠ cient algorithms take advantage of such factorization Factorization can be visualized as a factor graph
Example Bipartite graph over variables and local functions Edge “is an argument of” relation Encodes an e ff٠ cient algorithm

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Bayes Nets to Factor Graphs f A (x 1 ) = p(x 1 ) f B (x 2 ) = p(x 2 ) f C (x 1 ,x 2 ,x 3 ) = p(x 3 |x 1 ,x 2 ) f D (x 3 ,x 4 ) = p(x 4 |x 3 ) Instructor: Arindam Banerjee f E (x 3 ,x 5 ) = p(x 5 |x 3 ) The Sum-Product Algorithm
Marginalize Product of Functions Many problems involve “marginalize product of functions” (MPF) Inference in Bayesian networks Compute p(x 1 |x 4 ,x 5 ) Need to compute p(x 1 ,x 4 ,x 5 ) and p(x 4 ,x 5 ) Marginalization of joint distribution is a MPF problem Several other problems use MPF Prediction/Filtering in dynamic Bayes nets Viterbi decoding in hidden Markov models Error correcting codes

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Marginalize Product of Functions (Contd.)
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