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

Muneki Yasuda, Shun Kataoka

研究成果: Article査読

抄録

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.

本文言語English
論文番号084806
ジャーナルjournal of the physical society of japan
86
8
DOI
出版ステータスPublished - 2017 8 15

ASJC Scopus subject areas

  • 物理学および天文学(全般)

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