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Article: On Convergence Conditions of Gaussian Belief Propagation

TitleOn Convergence Conditions of Gaussian Belief Propagation
Authors
Issue Date2015
Citation
IEEE Transactions on Signal Processing, 2015, v. 63, p. 1144-1155 How to Cite?
AbstractIn order to compute the marginal probability density function (PDF) with Gaussian belief propagation (BP), it is impor- tant to know whether it will converge in advance. By describing the message-passing process of Gaussian BP on the pairwise factor graph as a set of updating functions, the necessary and sufficient convergence condition of beliefs in synchronous Gaussian BP is first derived under a newly proposed initialization set. The pro- posed initialization set is proved to be largest among all currently known sets. Then, the necessary and sufficient convergence con- dition of beliefs in damped Gaussian BP is developed, with the allowable range of damping factor explicitly established. The re- sults theoretically confirm the extensively reported conjecture that damping is helpful to improve the convergence of Gaussian BP. Under totally asynchronous scheduling, a sufficient convergence condition of beliefs is also derived for the same proposed initializa- tion set. Relationships between the proposed convergence condi- tions and existing ones are established analytically. At last, numer- ical examples are presented to corroborate the established theories.
Persistent Identifierhttp://hdl.handle.net/10722/214163

 

DC FieldValueLanguage
dc.contributor.authorSU, Q-
dc.contributor.authorWu, YC-
dc.date.accessioned2015-08-21T10:51:23Z-
dc.date.available2015-08-21T10:51:23Z-
dc.date.issued2015-
dc.identifier.citationIEEE Transactions on Signal Processing, 2015, v. 63, p. 1144-1155-
dc.identifier.urihttp://hdl.handle.net/10722/214163-
dc.description.abstractIn order to compute the marginal probability density function (PDF) with Gaussian belief propagation (BP), it is impor- tant to know whether it will converge in advance. By describing the message-passing process of Gaussian BP on the pairwise factor graph as a set of updating functions, the necessary and sufficient convergence condition of beliefs in synchronous Gaussian BP is first derived under a newly proposed initialization set. The pro- posed initialization set is proved to be largest among all currently known sets. Then, the necessary and sufficient convergence con- dition of beliefs in damped Gaussian BP is developed, with the allowable range of damping factor explicitly established. The re- sults theoretically confirm the extensively reported conjecture that damping is helpful to improve the convergence of Gaussian BP. Under totally asynchronous scheduling, a sufficient convergence condition of beliefs is also derived for the same proposed initializa- tion set. Relationships between the proposed convergence condi- tions and existing ones are established analytically. At last, numer- ical examples are presented to corroborate the established theories.-
dc.languageeng-
dc.relation.ispartofIEEE Transactions on Signal Processing-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleOn Convergence Conditions of Gaussian Belief Propagation-
dc.typeArticle-
dc.identifier.emailWu, YC: ycwu@eee.hku.hk-
dc.identifier.authorityWu, YC=rp00195-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1109/TSP.2015.2389755-
dc.identifier.hkuros248924-
dc.identifier.volume63-
dc.identifier.spage1144-
dc.identifier.epage1155-

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