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题名: Partition function loop series for a general graphical model: free-energy corrections and message-passing equations
作者: Xiao, JQ ;  Zhou, HJ
刊名: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
出版日期: 2011
卷号: 44, 期号:42, 页码:425001
关键词: EXPANSIONS ;  LATTICE ;  SPIN
学科分类: Physics
通讯作者: Xiao, JQ (reprint author), Chinese Acad Sci, Inst Theoret Phys, Key Lab Frontiers Theoret Phys, Beijing 100190, Peoples R China.
部门归属: [Xiao, Jing-Qing; Zhou, Haijun] Chinese Acad Sci, Inst Theoret Phys, Key Lab Frontiers Theoret Phys, Beijing 100190, Peoples R China; [Xiao, Jing-Qing] Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, 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.
收录类别: SCI
原文出处: 查看原文
语种: 英语
WOS记录号: WOS:000295876700001
Citation statistics: 
内容类型: 期刊论文
URI标识: http://ir.itp.ac.cn/handle/311006/14247
Appears in Collections:理论物理所2011年知识产出_期刊论文

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Recommended Citation:
Xiao, JQ,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.
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