Year: 2021
Type: article
Abstract: Spatial Monte Carlo integration (SMCI) is an extension of standard Monte Carlo integration and can approximate expectations on Markov random fields with high accuracy. SMCI was applied to pairwise Boltzmann machine (PBM) learning, achieving superior results over those of some existing methods. The approximation level of SMCI can be altered, and it was proved that a higher-order approximation of SMCI is statistically more accurate than a lower-order approximation. However, SMCI as proposed in previous studies suffers from a limitation that prevents the application of a higher-order method to dense systems. This study makes two contributions. First, a generalization of SMCI (called generalized SMCI (GSMCI)) is proposed, which allows a relaxation of the above-mentioned limitation; moreover, a statistical accuracy bound of GSMCI is proved. Second, a new PBM learning method based on SMCI is proposed, which is obtained by combining SMCI and persistent contrastive divergence. The proposed learning method significantly improves learning accuracy.
Source: Neural Computation
DOI: 10.1162/neco_a_01365
Authors: Muneki Yasuda, Kei Uchizawa
Institution: Yamagata University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3083074142