文章基本信息

标题：Solvable Probabilistic Model for Cycles in Planar Graph
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作者：Kazuyuki TANAKA ; Valery VAN KERREBROECK
期刊名称：Interdisciplinary Information Sciences
印刷版ISSN：1340-9050
电子版ISSN：1347-6157
出版年度：2009
卷号：15
期号：2
页码：301-318
DOI：10.4036/iis.2009.301
出版社：The Editorial Committee of the Interdisciplinary Information Sciences
摘要：We study a probabilistic model for single connected cycles on an undirected planar graph for which the degree of every vertex is restricted to two or three. By using a diagrammatical method to solve a free fermion model, we derive the exact expression of the partition function as well as marginal probabilities. We compare the exact results for the marginals with the approximations obtained with Loopy Belief Propagation allowing us to evaluate the efficacy of the latter.
关键词：probabilistic information processing;statistical inference;Bayesian network;free fermion model;loopy belief propagation;statistical mechanics;advanced mean-field method