TY - JOUR

T1 - Solving non-parametric inverse problem in continuous Markov random field using loopy belief propagation

AU - Yasuda, Muneki

AU - Kataoka, Shun

N1 - Funding Information:
This work was partially supported by JST CREST Grant Number JPMJCR1402 and by JSPS KAKENHI Grant Numbers 15K00330, 15H03699, and 15K20870.
Publisher Copyright:
©2017 The Physical Society of Japan.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2017/8/15

Y1 - 2017/8/15

N2 - In this paper, we address the inverse problem, or the statistical machine learning problem, in Markov random fields with a non-parametric pair-wise energy function with continuous variables. The inverse problem is formulated by maximum likelihood estimation. The exact treatment of maximum likelihood estimation is intractable because of two problems: (1) it includes the evaluation of the partition function and (2) it is formulated in the form of functional optimization. We avoid Problem (1) by using Bethe approximation. Bethe approximation is an approximation technique equivalent to the loopy belief propagation. Problem (2) can be solved by using orthonormal function expansion. Orthonormal function expansion can reduce a functional optimization problem to a function optimization problem. Our method can provide an analytic form of the solution of the inverse problem within the framework of Bethe approximation as a result of variational optimization.

AB - In this paper, we address the inverse problem, or the statistical machine learning problem, in Markov random fields with a non-parametric pair-wise energy function with continuous variables. The inverse problem is formulated by maximum likelihood estimation. The exact treatment of maximum likelihood estimation is intractable because of two problems: (1) it includes the evaluation of the partition function and (2) it is formulated in the form of functional optimization. We avoid Problem (1) by using Bethe approximation. Bethe approximation is an approximation technique equivalent to the loopy belief propagation. Problem (2) can be solved by using orthonormal function expansion. Orthonormal function expansion can reduce a functional optimization problem to a function optimization problem. Our method can provide an analytic form of the solution of the inverse problem within the framework of Bethe approximation as a result of variational optimization.

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U2 - 10.7566/JPSJ.86.084806

DO - 10.7566/JPSJ.86.084806

M3 - Article

AN - SCOPUS:85026426169

VL - 86

JO - Journal of the Physical Society of Japan

JF - Journal of the Physical Society of Japan

SN - 0031-9015

IS - 8

M1 - 084806

ER -