PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Loop corrected belief propagation
Joris Mooij, Bastian Wemmenhove, Bert Kappen and Tommaso Rizzo
Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics (AISTATS-07) 2007.

Abstract

We propose a method for improving Belief Propagation (BP) that takes into account the influence of loops in the graphical model. The method is a variation on and generalization of the method recently introduced by (Montanari and Rizzo, 2005). It consists of two steps: (i) standard BP is used to calculate cavity distributions for each variable (i.e. probability distributions on the Markov blanket of a variable for a modified graphical model, in which the factors involving that variable have been removed); (ii) all cavity distributions are combined by a message-passing algorithm to obtain consistent single node marginals. The method is exact if the graphical model contains a single loop. The complexity of the method is exponential in the size of the Markov blankets. The results are very accurate in general: the error is often several orders of magnitude smaller than that of standard BP, as illustrated by numerical experiments.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:3216
Deposited By:Joris Mooij
Deposited On:20 January 2008