Knowledge Management System of Institute of Theoretical Physics, CAS
Xiao, JQ; Zhou, HJ; Xiao, JQ (reprint author), Chinese Acad Sci, Inst Theoret Phys, Key Lab Frontiers Theoret Phys, Beijing 100190, Peoples R China. | |
Partition function loop series for a general graphical model: free-energy corrections and message-passing equations | |
Source Publication | JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL |
Language | 英语 |
Keyword | Expansions Lattice Spin |
Abstract | 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. |
2011 | |
ISSN | 1751-8113 |
Volume | 44Issue:42Pages:425001 |
Subject Area | Physics |
Indexed By | SCI |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.itp.ac.cn/handle/311006/14247 |
Collection | SCI期刊论文 |
Corresponding Author | Xiao, JQ (reprint author), Chinese Acad Sci, Inst Theoret Phys, Key Lab Frontiers Theoret Phys, Beijing 100190, Peoples R China. |
Recommended Citation GB/T 7714 | Xiao, JQ,Zhou, HJ,Xiao, JQ . 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 | Xiao, JQ,Zhou, HJ,&Xiao, JQ .(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 | Xiao, JQ,et al."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. |
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