文章基本信息

标题：Harnessing the Bethe Free Energy
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作者：Victor Bapst ; Amin Coja-Oghlan
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2015
卷号：40
页码：467-480
DOI：10.4230/LIPIcs.APPROX-RANDOM.2015.467
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：Gibbs measures induced by random factor graphs play a prominent role in computer science, combinatorics and physics. A key problem is to calculate the typical value of the partition function. According to the "replica symmetric cavity method", a heuristic that rests on non-rigorous considerations from statistical mechanics, in many cases this problem can be tackled by way of maximising a functional called the "Bethe free energy". In this paper we prove that the Bethe free energy upper-bounds the partition function in a broad class of models. Additionally, we provide a sufficient condition for this upper bound to be tight.
关键词：Belief Propagation; free energy; Gibbs measure; partition function