TY - JOUR
T1 - Statistical analysis of loopy belief propagation in random fields
AU - Yasuda, Muneki
AU - Kataoka, Shun
AU - Tanaka, Kazuyuki
N1 - Publisher Copyright:
© 2015 American Physical Society.
Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015/10/8
Y1 - 2015/10/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84945237234&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84945237234&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.92.042120
DO - 10.1103/PhysRevE.92.042120
M3 - Article
AN - SCOPUS:84945237234
VL - 92
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 4
M1 - 042120
ER -