A Numerical Analysis of Learning Coefficient in Radial Basis Function Network

Abstract

The radial basis function (RBF) network is a regression model that uses the sum of radial basis functions such as Gaussian functions. It has recently been widely applied to spectral deconvolution such as X-ray photoelectron spectroscopy data analysis, which enables us to estimate the electronic state of matter from the spectral peak positions. For models with a hierarchy such as the RBF network, Bayesian learning provides better generalization performance than the maximum likelihood estimation. In Bayesian learning, the learning coefficient is well-known as the coefficients of the leading terms for the asymptotic expansion of generalization error and stochastic complexity. However, these coefficients have not been clarified in most models. We propose here a novel method for calculating the learning coefficient by using the exchange Monte Carlo method. In addition, we calculated the learning coefficient in the RBF networks and verified the efficiency of the proposed method by comparing theoretical and experimental values.