A Family of Probabilistic Kernels Based on Information Divergence

Abstract

Probabilistic kernels offer a way to combine generative models with discriminative classifiers. We establish connections between probabilistic kernels and feature space kernels through a geometric interpretation of the previously proposed probability product kernel. A family of probabilistic kernels, based on information divergence measures, is then introduced and its connections to various existing probabilistic kernels are analyzed. The new family is shown to provide a unifying framework for the study of various important questions in kernel theory and practice. We exploit this property to design a set of experiments that yield interesting results regarding the role of properties such as linearity, positive definiteness, and the triangle inequality in kernel performance.