Advances in Nonparametric Bayesian Methods for Clustering and Classification

Abstract

Nonparametric Bayesian methods have proven to be extremely useful due to their flexibility and applicability to a wide range of problems. The first problem is motivated by a computer security problem, and a nonparametric Bayesian model is proposed by implementing the Dirichlet process mixture (DPM) prior for classifying programs as benign or malicious and simultaneously clustering malicious programs. In the second problem, we propose a new method for the fundamental task of testing for dependence between two groups of variables. The response densities under the null hypothesis of independence and the alternative hypothesis of dependence are specified by nonparametric Bayesian models. Under the null hypothesis, the joint distribution is modeled by the product of two independent DPM priors; under the alternative, the full joint density is modeled by a DPM prior. The test is then based on the posterior probability of favoring the alternative hypothesis. The last part, I will introduce an efficient density estimation method for high dimensional problems. Our proposed model first factorizes the original dimensions to several lower-dimensional groups, and uses the DPM prior to model the lower-dimensional densities. Our results show that when such a low-dimensional structure exists, the proposed model is more efficient than competing methods.