Bayesian Wavelet Networks for Nonparametric Regression

Radial wavelet networks have recently been proposed as a method for nonparametric regression. In this paper we analyze their performance within a Bayesian framework. We derive probability distributions over both the dimension of the networks and the network coefficients by placing a prior on the degrees of freedom of the model. This process bypasses the need to test or select a finite number of networks during the modeling process. Predictions are formed by mixing over many models of varying dimension and parameterization. We show that the complexity of the models adapts to the complexity of the data and produces good results on a number of benchmark test series. Index Terms--Bayesian neural networks, Markov chain Monte Carlo, model choice, nonparametric regression, radial basis functions, reversible jump, splines, wavelets.