Statistical analysis of loopy belief propagation in random fields

Muneki Yasuda, Shun Kataoka, Kazuyuki Tanaka

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Loopy belief propagation (LBP), which is equivalent to the Bethe approximation in statistical mechanics, is a message-passing-type inference method that is widely used to analyze systems based on Markov random fields (MRFs). In this paper, we propose a message-passing-type method to analytically evaluate the quenched average of LBP in random fields by using the replica cluster variation method. The proposed analytical method is applicable to general pairwise MRFs with random fields whose distributions differ from each other and can give the quenched averages of the Bethe free energies over random fields, which are consistent with numerical results. The order of its computational cost is equivalent to that of standard LBP. In the latter part of this paper, we describe the application of the proposed method to Bayesian image restoration, in which we observed that our theoretical results are in good agreement with the numerical results for natural images.

Original languageEnglish
Article number042120
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number4
Publication statusPublished - 2015 Oct 8

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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