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

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. © Springer-Verlag Berlin Heidelberg 2006.