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arXiv · 2006.15363

$α$ Belief Propagation for Approximate Inference

Dong Liu·Minh Thành Vu·Zuxing Li·Lars K. Rasmussen
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Abstract

Belief propagation (BP) algorithm is a widely used message-passing method for inference in graphical models. BP on loop-free graphs converges in linear time. But for graphs with loops, BP's performance is uncertain, and the understanding of its solution is limited. To gain a better understanding of BP in general graphs, we derive an interpretable belief propagation algorithm that is motivated by minimization of a localized $α$-divergence. We term this algorithm as $α$ belief propagation ($α$-BP). It turns out that $α$-BP generalizes standard BP. In addition, this work studies the convergence properties of $α$-BP. We prove and offer the convergence conditions for $α$-BP. Experimental simulations on random graphs validate our theoretical results. The application of $α$-BP to practical problems is also demonstrated.

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Dong Liu, Minh Thành Vu, Zuxing Li, Lars K. Rasmussen. 2020-06-27. $α$ Belief Propagation for Approximate Inference. https://arxiv.org/abs/2006.15363

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