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

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
Sum-Product Algorithm CSci 5512: Artifcial Intelligence II
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Factor Graphs Many problems deal with global function of many variables Global function “factors” into product of local functions E f cient algorithms take advantage of such factorization Factorization can be visualized as a factor graph
Background image of page 2
Example Bipartite graph over variables and local functions Edge “is an argument of” relation Encodes an e f cient algorithm
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 21

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online