Loop-corrected belief propagation for lattice spin models

Hai-Jun Zhou; Wei-Mou Zheng

doi:10.1140/epjb/e2015-60485-6

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arXiv · 1505.03504

Loop-corrected belief propagation for lattice spin models

Hai-Jun Zhou·Wei-Mou Zheng

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Abstract

Belief propagation (BP) is a message-passing method for solving probabilistic graphical models. It is very successful in treating disordered models (such as spin glasses) on random graphs. On the other hand, finite-dimensional lattice models have an abundant number of short loops, and the BP method is still far from being satisfactory in treating the complicated loop-induced correlations in these systems. Here we propose a loop-corrected BP method to take into account the effect of short loops in lattice spin models. We demonstrate, through an application to the square-lattice Ising model, that loop-corrected BP improves over the naive BP method significantly. We also implement loop-corrected BP at the coarse-grained region graph level to further boost its performance.

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cond-mat.stat-mech cond-mat.dis-nn cs.CV

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BibTeX RIS

Hai-Jun Zhou, Wei-Mou Zheng. 2016-02-16. Loop-corrected belief propagation for lattice spin models. https://doi.org/10.1140/epjb%2Fe2015-60485-6

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