Generalization Error of Three Layered Learning Model in Bayesian Estimation

M. Aoyagi and S. Watanabe (Japan)

Keywords

Generalization error, nonregular learning machines, Bayesian estimate, resolution of singularities, Kullback function, zeta function.

Abstract

In this paper, we obtain the asymptotic forms of the gen eralization errors for some three layered learning models in Bayesian estimation. The generalization error measures how precisely learning models can approximate true den sity functions which produce learning data. We use a recur sive blowing up process for analyzing the Kullback func tion of the learning model. Then, we have the maximum pole of its zeta function which is deļ¬ned 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.

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