Learning Coefficients and Reproducing True Probability Functions in Learning Systems

Abstract

Recently, the widely applicable information criterion (WAIC) model selection method has been considered for reproducing and estimating a probability function from data in a learning system. The learning coefficient in Bayesian estimation serves to measure the learning efficiency in singular learning models, and has an important role in the WAIC method. Mathematically, the learning coefficient is the log canonical threshold of the relative entropy. In this paper, we consider the Vandermonde matrix-type singularity learning coefficients in statistical learning theory.