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Convergence analysis of belief propagation for pairwise linear Gaussian models
Du J.1; Ma S.3; Wu Y.-C.2; Kar S.1; Moura J.M.F.1
2018-03-07
Conference Name2017 IEEE GLOBAL CONFERENCE ON SIGNAL AND INFORMATION PROCESSING (GLOBALSIP 2017)
Source Publication2017 IEEE Global Conference on Signal and Information Processing, GlobalSIP 2017 - Proceedings
Volume2018-January
Pages548-552
Conference DateNOV 14-16, 2017
Conference PlaceMontreal, CANADA
Abstract

Gaussian belief propagation (BP) has been widely used for distributed inference in large-scale networks such as the smart grid, sensor networks, and social networks, where local measurements/observations are scattered over a wide geographical area. One particular case is when two neighboring agents share a common observation. For example, to estimate voltage in the direct current (DC) power flow model, the current measurement over a power line is proportional to the voltage difference between two neighboring buses. When applying the Gaussian BP algorithm to this type of problem, the convergence condition remains an open issue. In this paper, we analyze the convergence properties of Gaussian BP for this pairwise linear Gaussian model. We show analytically that the updating information matrix converges at a geometric rate to a unique positive definite matrix with arbitrary positive semidefinite initial value and further provide the necessary and sufficient convergence condition for the belief mean vector to the optimal estimate.

KeywordBelief Propagation Distributed Inference Graphical Model Large-scale Networks Markov Random Field
DOI10.1109/GlobalSIP.2017.8308703
URLView the original
Indexed BySCI
Language英语
WOS Research AreaEngineering
WOS SubjectEngineering, Electrical & Electronic
WOS IDWOS:000450053100110
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Document TypeConference paper
专题DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING
Affiliation1.Carnegie Mellon University
2.The University of Hong Kong
3.Universidade de Macau
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Du J.,Ma S.,Wu Y.-C.,et al. Convergence analysis of belief propagation for pairwise linear Gaussian models[C],2018:548-552.
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