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Unformatted text preview: Approximate Inference CSci 5512: ArtiFcial Intelligence II Bayesian Networks with Loops A direct application of sumproduct can be problematic Can be converted to a junction tree, size can be exponential Focus on approximate inference techniques: Stochastic inference, based on sampling Deterministic inference, based on approximations Cloudy Wet Grass Rain Sprinkler T F .80 .20 C P(RC) T F .10 .5 C P(SC) T T F F T F T F P(C) .50 .99 .90 .90 .01 S R P(WS,R) Inference by Stochastic Simulation Basic idea: Draw N samples from a sampling distribution Compute an approximate posterior probability Pˆ Show this converges to the true probability P Sampling approaches: Sampling from an empty network Rejection sampling Likelihood weighting Markov chain Monte Carlo (MCMC) P(X 1 ,...,X n ) = Sampling from an empty network Consider a Bayesian Network P(X 1 ,...,X n ) The joint distribution factorizes as n P(X i Parents(X i )) i=1 For i = 1,...,n Assume Parent s(X i ) have been instantiated Draw a sample x i following P(X i Parents(X i )) (x 1 ,...,x n ) forms a sample from the Bayesian Network Example Cloudy Wet Grass Rain Sprinkler T F .80 .20 C P(RC) T F .10 .5 C P(SC) T T F F T F T F P(C) .50 .99 .90 .90 .01 S R P(WS,R) Example Cloudy Wet Grass Rain Sprinkler T F .80 .20 C P(RC) T F .10 .5 C P(SC) T T F F T F T F P(C) .50 .99 .90 .90 .01 S R P(WS,R) Example Cloudy Wet Grass Rain Sprinkler T F C P(RC) T F C P(SC) T T F F T F T F P(C) .50 .99 .90 .90 .01 S R P(WS,R) .10 .5 .80 .20 Example Cloudy Wet Grass Rain Sprinkler T F C P(RC) T F C P(SC) T T F F T F T F P(C) .50 .99 .90 .90 .01 S R P(WS,R) .10 .5 .80 .20 Example...
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This note was uploaded on 02/07/2012 for the course CSCI 5512 taught by Professor Staff during the Spring '08 term at Minnesota.
 Spring '08
 Staff
 Artificial Intelligence

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