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.
%0 Journal Article
%1 Zhou2016Loopcorrected
%A Zhou, Hai-Jun
%A Zheng, Wei-Mou
%D 2016
%J The European Physical Journal B
%K cycles, message-passing, spin-models lattice-models
%N 12
%R 10.1140/epjb/e2015-60485-6
%T Loop-corrected belief propagation for lattice spin models
%U http://dx.doi.org/10.1140/epjb/e2015-60485-6
%V 88
%X 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.
@article{Zhou2016Loopcorrected,
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.}},
added-at = {2019-06-10T14:53:09.000+0200},
archiveprefix = {arXiv},
author = {Zhou, Hai-Jun and Zheng, Wei-Mou},
biburl = {https://www.bibsonomy.org/bibtex/23a84a01b1f2fba1c82dfb7314b6c72b2/nonancourt},
citeulike-article-id = {13611545},
citeulike-linkout-0 = {http://dx.doi.org/10.1140/epjb/e2015-60485-6},
citeulike-linkout-1 = {http://arxiv.org/abs/1505.03504},
citeulike-linkout-2 = {http://arxiv.org/pdf/1505.03504},
citeulike-linkout-3 = {http://dx.doi.org/10.1140/epjb/e2015-60485-6},
day = 16,
doi = {10.1140/epjb/e2015-60485-6},
eprint = {1505.03504},
interhash = {bcc21d7ba0c80ec2b54d9644df375139},
intrahash = {3a84a01b1f2fba1c82dfb7314b6c72b2},
issn = {1434-6036},
journal = {The European Physical Journal B},
keywords = {cycles, message-passing, spin-models lattice-models},
month = dec,
number = 12,
posted-at = {2015-05-14 11:29:58},
priority = {2},
timestamp = {2019-08-01T15:36:09.000+0200},
title = {{Loop-corrected belief propagation for lattice spin models}},
url = {http://dx.doi.org/10.1140/epjb/e2015-60485-6},
volume = 88,
year = 2016
}