Generalization error of three layered learning model in bayesian estimation

In this paper, we obtain the asymptotic forms of the generalization errors for some three layered learning models in Bayesian estimation. The generalization error measures how precisely learning models can approximate true density functions which produce learning data. We use a recursive blowing up process for analyzing the Kullback function of the learning model. Then, we have the maximum pole of its zeta function which is defined by the integral of the Kullback function and an a priori probability density function. In [1, 2], it was proved that the maximum pole of the zeta function asymptotically gives the generalization error of the hierarchical learning model.