Mixed-Membership Naive Bayes Models

Abstract

In recent years, mixture models have found widespread usage in discovering latent cluster structure from data. A popular special case of finite mixture models are naive Bayes models, where the probability of a feature vector factorizes over the features for any given component of the mixture. Despite their popularity, naive Bayes models suffer from two important restrictions: first, they do not have a natural mechanism for handling sparsity, where each data point may have only a few observed features; and second, they do not allow objects to be generated from different latent clusters with varying degrees (i.e., mixed-memberships) in the generative process. In this paper, we first introduce marginal naive Bayes (MNB) models, which generalize naive Bayes models to handle sparsity by marginalizing over all missing features. More importantly, we propose mixed-membership naive Bayes (MMNB) models, which generalizes (marginal) naive Bayes models to allow for mixed memberships in the generative process. MMNB models can be viewed as a natural generalization of latent Dirichlet allocation (LDA) with the ability to handle heterogenous and possibly sparse feature vectors. We propose two variational inference algorithms to learn MMNB models from data. While the first exactly follows the corresponding ideas for LDA, the second uses much fewer variational parameters leading to a much faster algorithm with smaller time and space requirements. An application of the same idea in the context of topic modeling leads to a new Fast LDA algorithm. The efficacy of the proposed mixed-membership models and the fast variational inference algorithms are demonstrated by extensive experiments on a wide variety of different datasets.