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# Particle Belief Propagation

*Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics*, PMLR 5:256-263, 2009.

#### Abstract

The popularity of particle filtering for inference in Markov chain models defined over random variables with very large or continuous domains makes it natural to consider sample–based versions of belief propagation (BP) for more general (tree–structured or loopy) graphs. Already, several such algorithms have been proposed in the literature. However, many questions remain open about the behavior of particle–based BP algorithms, and little theory has been developed to analyze their performance. In this paper, we describe a generic particle belief propagation (PBP) algorithm which is closely related to previously proposed methods. We prove that this algorithm is consistent, approaching the true BP messages as the number of samples grows large. We then use concentration bounds to analyze the finite-sample behavior and give a convergence rate for the algorithm on tree–structured graphs. Our convergence rate is $O(1/\sqrt{n})$ where n is the number of samples, independent of the domain size of the variables.