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

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

View Full Document Right Arrow Icon
Click to edit Master subtitle style 10/25/10 Exact Inference in Bayes Nets
Background image of page 1

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

View Full DocumentRight Arrow Icon
10/25/10 Inference Techniques § Exact Inference § Variable elimination § Belief propagation (polytrees) § Junction tree algorithm (arbitrary graphs) § Kalman filte § § 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
Background image of page 2
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
Background image of page 3

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

View Full DocumentRight Arrow Icon
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 ) , , ( ) , , ( ) , ( ) , ( ) | (
Background image of page 4
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)
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.

This note was uploaded on 10/24/2010 for the course CSCI 4202 at Colorado.

Page1 / 22

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

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