Stochastic Complexity and Generalization Error of a Restricted Boltzmann Machine in Bayesian Estimation

In this paper, we consider the asymptotic form of the generalization error for the restricted Boltzmann machine in Bayesian estimation. It has been shown that obtaining the maximum pole of zeta functions is related to the asymptotic form of the generalization error for hierarchical learning models (Watanabe, 2001a,b). The zeta function is defined by using a Kullback function. We use two methods to obtain the maximum pole: a new eigenvalue analysis method and a recursive blowing up process. We show that these methods are effective for obtaining the asymptotic form of the generalization error of hierarchical learning models.