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Inference1 - Exact Inference in Bayes Nets Click to edit...

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Click to edit Master subtitle style 10/25/10 Exact Inference in Bayes Nets
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10/25/10 Inference Techniques § Exact Inference § Variable elimination § Belief propagation (polytrees) § Junction tree algorithm (arbitrary graphs) § Kalman filte § Adams & MacKay changepoint § Approximate Inference § Loopy belief propagation § Rejection sampling § Importance sampling § Markov Chain Monte Carlo (MCMC) § Gibbs sampling § Variational approximations § Expectation maximization (forward-backward algorithm) § Particle filters Later in the semester
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10/25/10 Notation U: set of nodes in a graph Xi: random variable associated with node i πi: parents of node i Joint probability: General form to include undirected as well as directed graphs: where C is an index over cliques to apply to directed graph, turn directed graph into moral graph moral graph: connect all parents of each node and remove arrows
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10/25/10 Common Inference Problems Assume partition of graph into subsets O = observations; U = unknowns; N = nuisance variables Computing marginals (avg. over nuisance vars.) Computing MAP probability Given observations O, find distribution over U = N x N U U x x p x p ) , ( ) ( ) , ( max ) ( * N U x U x x p x p N = ∑ ∑ = = U N N U x x N O U x N O U x O U O U O U x x x p x x x p x x p x x p x x p ) , , ( ) , , ( ) , ( ) , ( ) | (
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10/25/10 Variable Elimination E.g., calculating marginal p(x5) Elimination order: 1, 2, 4, 3 m12( x2) m23( x3) m43( x3) m35( x5)
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10/25/10
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