Unformatted text preview: nalize Product of Functions Many problems involve “marginalize product of functions”
(MPF)
Inference in Bayesian networks
Compute p (x1 x4 , x5 )
Need to compute p (x1 , x4 , x5 ) and p (x4 , x5 ) Instructor: Arindam Banerjee The SumProduct Algorithm Marginalize Product of Functions Many problems involve “marginalize product of functions”
(MPF)
Inference in Bayesian networks
Compute p (x1 x4 , x5 )
Need to compute p (x1 , x4 , x5 ) and p (x4 , x5 )
Marginalization of joint distribution is a MPF problem Instructor: Arindam Banerjee The SumProduct Algorithm Marginalize Product of Functions Many problems involve “marginalize product of functions”
(MPF)
Inference in Bayesian networks
Compute p (x1 x4 , x5 )
Need to compute p (x1 , x4 , x5 ) and p (x4 , x5 )
Marginalization of joint distribution is a MPF problem Several other problems use MPF Instructor: Arindam Banerjee The SumProduct Algorithm Marginalize Product of Functions Many problems involve “marginalize product of functions”
(MPF)
Inference in Bayesian networks
Compute p (x1 x4 , x5 )
Need to compute p (x1 , x4 , x5 ) and p (x4 , x5 )
Marginalization of joint distribution is a MPF problem Several other problems use MPF
Prediction/Filtering in dynamic Bayes nets Instructor: Arindam Banerjee The SumProduct Algorithm Marginalize Product of Functions Many problems involve “marginalize product of functions”
(MPF)
Inference in Bayesian networks
Compute p (x1 x4 , x5 )
Need to compute p (x1 , x4 , x5 ) and p (x4 , x5 )
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 Instructor: Arindam Banerjee The SumProduct Algorithm Marginalize Product of Functions Many problems involve “marginalize product of functions”
(MPF)
Inference in Bayesian networks
Compute p (x1 x4 , x5 )
Need to compute p (x1 , x4 , x5 ) and p (x4 , x5 )
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 Instructor: Arindam Banerjee The SumProduct Algorithm Marginalize Product of Fun...
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 Fall '11
 AbhishekChanda
 Bayesian network, factor graph, graphical model, Belief propagation, Arindam Banerjee, sumproduct algorithm

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