Fixing convergence of Gaussian belief propagation

Jason K. Johnson, Danny Bickson, Danny Dolev

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

27 Scopus citations

Abstract

Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple sufficient conditions for its convergence have been established. In this paper we develop a double-loop algorithm for forcing convergence of GaBP. Our method computes the correct MAP estimate even in cases where standard GaBP would not have converged. We further extend this construction to compute least-squares solutions of over-constrained linear systems. We believe that our construction has numerous applications, since the GaBP algorithm is linked to solution of linear systems of equations, which is a fundamental problem in computer science and engineering. As a case study, we discuss the linear detection problem. We show that using our new construction, we are able to force convergence of Montanari's linear detection algorithm, in cases where it would originally fail. As a consequence, we are able to increase significantly the number of users that can transmit concurrently.

Original languageEnglish
Title of host publication2009 IEEE International Symposium on Information Theory, ISIT 2009
Pages1674-1678
Number of pages5
DOIs
StatePublished - 2009
Event2009 IEEE International Symposium on Information Theory, ISIT 2009 - Seoul, Korea, Republic of
Duration: 28 Jun 20093 Jul 2009

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8102

Conference

Conference2009 IEEE International Symposium on Information Theory, ISIT 2009
Country/TerritoryKorea, Republic of
CitySeoul
Period28/06/093/07/09

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