Asymptotic behavior of stochastic complexity of complete bipartite graph-type boltzmann machines

Authors:
Yu Nishiyama;Sumio Watanabe
Affiliations:
Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama, Japan;Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama, Japan
Venue:
ICONIP'06 Proceedings of the 13 international conference on Neural Information Processing - Volume Part I
Year:
2006

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Singularities in complete bipartite graph-type Boltzmann machines and upper bounds of stochastic complexities

IEEE Transactions on Neural Networks

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Abstract

In singular statistical models, it was shown that Bayes learning is effective. However, on Bayes learning, calculation containing the Bayes posterior distribution requires huge computational costs. To overcome the problem, mean field approximation (or equally variational Bayes method) was proposed. Recently, the generalization error and stochastic complexity in mean field approximation have been theoretically studied. In this paper, we treat the complete bipartite graph-type Boltzmann machines and derive the upper bound of the asymptotic stochastic complexity in mean field approximation.