%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 }