Sum Product Algorithm

Product of functions many problems involve

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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 Sum-Product 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 Sum-Product 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 Sum-Product 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 Sum-Product 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 Sum-Product 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 Sum-Product Algorithm Marginalize Product of Fun...
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