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.
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March 2021
March 26 2021
A Generalization of Spatial Monte Carlo Integration
In Special Collection:
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Muneki Yasuda,
Muneki Yasuda
Graduate School of Science and Engineering, Yamagata University, Yonezawa, Yamagata 992-8510 Japan, [email protected]
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Kei Uchizawa
Kei Uchizawa
Graduate School of Science and Engineering, Yamagata University, Yonezawa, Yamagata 992-8510 Japan, [email protected]
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Muneki Yasuda
Graduate School of Science and Engineering, Yamagata University, Yonezawa, Yamagata 992-8510 Japan, [email protected]
Kei Uchizawa
Graduate School of Science and Engineering, Yamagata University, Yonezawa, Yamagata 992-8510 Japan, [email protected]
Received:
September 14 2020
Accepted:
October 28 2020
Online ISSN: 1530-888X
Print ISSN: 0899-7667
© 2021 Massachusetts Institute of Technology
2021
Massachusetts Institute of Technology
Neural Computation (2021) 33 (4): 1037–1062.
Article history
Received:
September 14 2020
Accepted:
October 28 2020
Citation
Muneki Yasuda, Kei Uchizawa; A Generalization of Spatial Monte Carlo Integration. Neural Comput 2021; 33 (4): 1037–1062. doi: https://doi.org/10.1162/neco_a_01365
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