Sparse regression mixture modeling with the multi-kernel relevance vector machine

Abstract

A regression mixture model is proposed where each mixture component is a multi-kernel version of the Relevance Vector Machine (RVM). This mixture model exploits the enhanced modeling capability of RVMs, due to their embedded sparsity enforcing properties. In order to deal with the selection problem of kernel parameters, a weighted multi-kernel scheme is employed, where the weights are estimated during training. The mixture model is trained using the maximum a posteriori approach, where the Expectation Maximization (EM) algorithm is applied offering closed form update equations for the model parameters. Moreover, an incremental learning methodology is also presented that tackles the parameter initialization problem of the EM algorithm along with a BIC-based model selection methodology to estimate the proper number of mixture components. We provide comparative experimental results using various artificial and real benchmark datasets that empirically illustrate the efficiency of the proposed mixture model.