Inverse Problem in Pairwise Markov Random Fields Using Loopy Belief Propagation

In this paper, using Chebyshev polynomials, we derive a new representation of loopy belief propagation for pairwise Markov random fields in terms of moments. Using the new representation, we propose a new method to solve a statistical inverse problem in pairwise Markov random fields within the frame...

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Bibliographic Details
Published in:Journal of the Physical Society of Japan 2012-04, Vol.81 (4), p.044801-044801-8
Main Authors: Yasuda, Muneki, Kataoka, Shun, Tanaka, Kazuyuki
Format: Article
Language:English
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Summary:In this paper, using Chebyshev polynomials, we derive a new representation of loopy belief propagation for pairwise Markov random fields in terms of moments. Using the new representation, we propose a new method to solve a statistical inverse problem in pairwise Markov random fields within the framework of loopy belief propagation. Our method allows us to solve the statistical inverse problem without any iterative operations. We numerically verify our method for the statistical inverse problem in $Q$-state Potts models.
ISSN:0031-9015
1347-4073
DOI:10.1143/JPSJ.81.044801