Partition function loop series for a general graphical model: free-energy corrections and message-passing equations

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	Partition function loop series for a general graphical model: free-energy corrections and message-passing equations
	Zhou, HJ
刊名	JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
	2011
卷号	44 期号:42 页码:425001
关键词	EXPANSIONS LATTICE SPIN
ISSN号	1751-8113
通讯作者	Xiao, JQ (reprint author), Chinese Acad Sci, Inst Theoret Phys, Key Lab Frontiers Theoret Phys, Beijing 100190, Peoples R China.
英文摘要	A loop series expansion for the partition function of a general statistical model on a graph is carried out. If the auxiliary probability distributions of the expansion are chosen to be a fixed point of the belief-propagation equation, the first term of the loop series gives the Bethe-Peierls (BP) free-energy functional at the replica-symmetric level of the mean-field spin-glass theory, and corrections are contributed only by subgraphs that are free of dangling edges. This result generalizes the early work of Chertkov and Chernyak on binary statistical models. If the belief-propagation equation has multiple fixed points, a loop series expansion is performed for the grand partition function. The first term of this series gives the BP free-energy functional at the first-step replica-symmetry-breaking (RSB) level of the mean-field spin-glass theory, and corrections again come only from subgraphs that are free of dangling edges, provided that the auxiliary probability distributions of the expansion are chosen to be a fixed point of the survey-propagation equation. The same loop series expansion can be performed for higher-level partition functions, obtaining the higher-level RSB BP free-energy functionals (and the correction terms) and message-passing equations without using the BP approximation.
学科主题	Physics
收录类别	SCI
原文出处	http://dx.doi.org/10.1088/1751-8113/44/42/425001
语种	英语
WOS记录号	WOS:000295876700001
公开日期	2013-05-17
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/14247]
专题	理论物理研究所_理论物理所1978-2010年知识产出
推荐引用方式 GB/T 7714	Zhou, HJ. Partition function loop series for a general graphical model: free-energy corrections and message-passing equations[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL,2011,44(42):425001.
APA	Zhou, HJ.(2011).Partition function loop series for a general graphical model: free-energy corrections and message-passing equations.JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL,44(42),425001.
MLA	Zhou, HJ."Partition function loop series for a general graphical model: free-energy corrections and message-passing equations".JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 44.42(2011):425001.