Time series prediction based on the Relevance Vector Machine with adaptive kernels

The Relevance Vector Machine (RVM) introduced by Tipping is a probabilistic model similar to the widespread Support Vector Machines (SVM), but where the training takes place in a Bayesian framework, and where predictive distributions of the outputs instead of point estimates are obtained. In this paper we focus on the use of RVM's for regression. We modify this method for training generalized linear models by adapting automatically the width of the basis functions to the optimal for the data at hand. Our Adaptive RVM is tried for prediction on the chaotic Mackey-Glass time series. Much superior performance than with the standard RVM and than with other methods like neural networks and local linear models is obtained.