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Sum Product Algorithm

# Sum Product Algorithm - The Sum-Product Algorithm CSci 5512...

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The Sum-Product Algorithm CSci 5512: Artificial Intelligence II Instructor: Arindam Banerjee February 1, 2010 Instructor: Arindam Banerjee The Sum-Product Algorithm

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Factor Graphs Many problems deal with global function of many variables Instructor: Arindam Banerjee The Sum-Product Algorithm
Factor Graphs Many problems deal with global function of many variables Global function “factors” into product of local functions Instructor: Arindam Banerjee The Sum-Product Algorithm

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Factor Graphs Many problems deal with global function of many variables Global function “factors” into product of local functions Efficient algorithms take advantage of such factorization Instructor: Arindam Banerjee The Sum-Product Algorithm
Factor Graphs Many problems deal with global function of many variables Global function “factors” into product of local functions Efficient algorithms take advantage of such factorization Factorization can be visualized as a factor graph Instructor: Arindam Banerjee The Sum-Product Algorithm

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Example Bipartite graph over variables and local functions Instructor: Arindam Banerjee The Sum-Product Algorithm
Example Bipartite graph over variables and local functions Edge “is an argument of” relation Instructor: Arindam Banerjee The Sum-Product Algorithm

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Example Bipartite graph over variables and local functions Edge “is an argument of” relation Encodes an efficient algorithm Instructor: Arindam Banerjee The Sum-Product Algorithm
Bayes Nets to Factor Graphs Instructor: Arindam Banerjee The Sum-Product 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 ) Instructor: Arindam Banerjee The Sum-Product Algorithm
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 ) f E ( x 3 , x 5 ) = p ( x 5 | x 3 ) Instructor: Arindam Banerjee The Sum-Product Algorithm

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Marginalize Product of Functions Many problems involve “marginalize product of functions” (MPF) Instructor: Arindam Banerjee The Sum-Product Algorithm
Marginalize Product of Functions Many problems involve “marginalize product of functions” (MPF) Inference in Bayesian networks Instructor: Arindam Banerjee The Sum-Product Algorithm

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Marginalize Product of Functions Many problems involve “marginalize product of functions” (MPF) Inference in Bayesian networks Compute p ( x 1 | x 4 , x 5 ) Instructor: Arindam Banerjee 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 ) Instructor: Arindam Banerjee The Sum-Product Algorithm

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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 Instructor: Arindam Banerjee The Sum-Product Algorithm
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• Fall '11
• AbhishekChanda
• Bayesian network, factor graph, graphical model, Belief propagation, Arindam Banerjee, sum-product algorithm

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