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...

A Bayesian-Kullback learning scheme, called Ying-Yang Machine, is proposed based on the two complement but equivalent Bayesian representations for joint density and their Kullback divergence. Not only the scheme unifies existing major supervised and unsupervised learnings, including the classical maximum likelihood or least square learning, the maximum information preservation, the EM & em algo...

In this paper, by conditioning on the matrix variate normal distribution (MVND) the construction of the matrix t-type family is considered, thus providing a new perspective of this family. Some important statistical characteristics are given. The presented t-type family is an extension to the work of Dickey [8]. A Bayes estimator for the column covariance matrix &Sigma of MVND is derived under ...