Deriving Probabilistic SVM Kernels from Exponential Family Approximations to Multivariate Distributions for Count Data

Abstract

This work aims to propose a robust hybrid probabilistic learning approach that combines appropriately the advantages of both the generative and discriminative models for modeling count data. We build new probabilistic kernels based on information divergences and Fisher score from efficient approximations to multivariate distributions for support vector machines (SVMs). More precisely, we drive probabilistic kernels from the mixture of exponential family approximation to two powerful generative models for count data, namely the multinomial compound Dirichlet (DCM) and the generalized Dirichlet multinomial (GDM). The developed hybrid models are introduced as effective SVM kernels able to incorporate prior knowledge about the nature of data involved in the problem at hand and, therefore, permits a good data discrimination. We demonstrate the flexibility and the merits of the proposed frameworks for the problem of analyzing activities in surveillance scenes.