A Comparison between the Tikhonov and the Bayesian Approaches to Calculate Regularisation Matrices

Abstract

Regularisation is a well-known technique for working with ill-posed and ill-conditioned problems that have been explored in a variety of different areas, including Bayesian inference, functional analysis, optimisation, numerical analysis and connectionist systems. In this paper we present the equivalence between the Bayesian approach to the regularisation theory and the Tikhonov regularisation into the function approximation theory framework, when radial basis functions networks are employed. This equivalence can be used to avoid expensive calculations when regularisation techniques are employed.