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.
Highlights
The machine learning techniques for Markov random fields (MRFs) are fundamental in various fields involving pattern recognition [1,2], image processing [3], sparse modeling [4], and Earth science [5,6], and a Boltzmann machine [7,8,9] is one of the most important models in MRFs.The inference and learning problems in the Boltzmann machine are NP-hard, because they include intractable multiple summations over all the possible configurations of variables
We examined the effectiveness of Boltzmann machine learning based on the 1-spatial Monte Carlo integration (SMCI)
Method proposed in [22] where, by numerical experiments, it was shown that the 1-SMCI learning method is more effective than the maximum pseudo-likelihood estimation (MPLE) in the case where no model error exists
Summary
The machine learning techniques for Markov random fields (MRFs) are fundamental in various fields involving pattern recognition [1,2], image processing [3], sparse modeling [4], and Earth science [5,6], and a Boltzmann machine [7,8,9] is one of the most important models in MRFs. This is one of the contributions of this paper.
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