A Bayesian Approach to Joint Feature Selection and Classifier Design.pdf

A Bayesian Approach to Joint Feature Selection and Classifier Design Balaji Krishnapuram,1,∗ Alexander J. Hartemink,2 Lawrence Carin,1 Fellow, ´ 3 IEEE , and Mario A. T. Figueiredo, Senior Member, IEEE Abstract This paper adopts a Bayesian approach to simultaneously learn both an optimal nonlinear classifier and a subset of predictor variables (or features) that are most relevant to the classification task. The approach uses heavy-tailed priors to promote sparsity in the utilization of both basis functions and features; these priors act as regularizers for the likelihood function that rewards good classification on the training data. We derive an expectation-maximization (EM) algorithm to efficiently compute a maximum a posteriori (MAP) point estimate of the various parameters. The algorithm is an extension of recent state-of-the- art sparse Bayesian classifiers, which in turn can be seen as Bayesian counterparts of support vector machines. Experimental comparisons using kernel classifiers demonstrate both parsimonious feature selection and excellent classification accuracy on a range of synthetic and benchmark datasets. Index Terms Statistical pattern recognition, statistical learning, feature selection, sparsity, support vector machines, relevance vector machines, sparse probit regression, automatic relevance determination, EM algorithm. I. INTRODUCTION A. Motivation In binary supervised learning problems, the goal is to learn how to distinguish between examples from