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Article: On Convergence Conditions of Gaussian Belief Propagation
Title | On Convergence Conditions of Gaussian Belief Propagation |
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Authors | |
Keywords | Convergence factor graph Gaussian belief propagation graphical model loopy belief propagation message passing sum-product algorithm |
Issue Date | 2015 |
Citation | IEEE Transactions on Signal Processing, 2015, v. 63, p. 1144-1155 How to Cite? |
Abstract | In 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 Identifier | http://hdl.handle.net/10722/214163 |
ISSN | 2023 Impact Factor: 4.6 2023 SCImago Journal Rankings: 2.520 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | SU, Q | - |
dc.contributor.author | Wu, YC | - |
dc.date.accessioned | 2015-08-21T10:51:23Z | - |
dc.date.available | 2015-08-21T10:51:23Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | IEEE Transactions on Signal Processing, 2015, v. 63, p. 1144-1155 | - |
dc.identifier.issn | 1053-587X | - |
dc.identifier.uri | http://hdl.handle.net/10722/214163 | - |
dc.description.abstract | In 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.language | eng | - |
dc.relation.ispartof | IEEE Transactions on Signal Processing | - |
dc.subject | Convergence | - |
dc.subject | factor graph | - |
dc.subject | Gaussian belief propagation | - |
dc.subject | graphical model | - |
dc.subject | loopy belief propagation | - |
dc.subject | message passing | - |
dc.subject | sum-product algorithm | - |
dc.title | On Convergence Conditions of Gaussian Belief Propagation | - |
dc.type | Article | - |
dc.identifier.email | Wu, YC: ycwu@eee.hku.hk | - |
dc.identifier.authority | Wu, YC=rp00195 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1109/TSP.2015.2389755 | - |
dc.identifier.scopus | eid_2-s2.0-84922816567 | - |
dc.identifier.hkuros | 248924 | - |
dc.identifier.volume | 63 | - |
dc.identifier.spage | 1144 | - |
dc.identifier.epage | 1155 | - |
dc.identifier.eissn | 1941-0476 | - |
dc.identifier.isi | WOS:000349159100006 | - |
dc.identifier.issnl | 1053-587X | - |