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Algorithms 2018, 11(4), 42; doi:10.3390/a11040042

Learning Algorithm of Boltzmann Machine Based on Spatial Monte Carlo Integration Method

Graduate School of Science and Engineering, Yamagata University, Yamagata 992-8510, Japan
Received: 28 February 2018 / Revised: 2 April 2018 / Accepted: 3 April 2018 / Published: 4 April 2018
(This article belongs to the Special Issue Monte Carlo Methods and Algorithms)
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Abstract

The machine learning techniques for Markov random fields are fundamental in various fields involving pattern recognition, image processing, sparse modeling, and earth science, and a Boltzmann machine is one of the most important models in Markov random fields. However, the inference and learning problems in the Boltzmann machine are NP-hard. The investigation of an effective learning algorithm for the Boltzmann machine is one of the most important challenges in the field of statistical machine learning. In this paper, we study Boltzmann machine learning based on the (first-order) spatial Monte Carlo integration method, referred to as the 1-SMCI learning method, which was proposed in the author’s previous paper. In the first part of this paper, we compare the method with the maximum pseudo-likelihood estimation (MPLE) method using a theoretical and a numerical approaches, and show the 1-SMCI learning method is more effective than the MPLE. In the latter part, we compare the 1-SMCI learning method with other effective methods, ratio matching and minimum probability flow, using a numerical experiment, and show the 1-SMCI learning method outperforms them. View Full-Text
Keywords: machine learning; Boltzmann machine; Monte Carlo integration; approximate algorithm machine learning; Boltzmann machine; Monte Carlo integration; approximate algorithm
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Yasuda, M. Learning Algorithm of Boltzmann Machine Based on Spatial Monte Carlo Integration Method. Algorithms 2018, 11, 42.

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