Hierarchical mixtures of Unigram models for short text clustering: the role of Beta-Liouville priors

This paper presents a variant of the Multinomial mixture model tailored for the unsupervised classification of short text data. Traditionally, the Multinomial probability vector in this hierarchical model is assigned a Dirichlet prior distribution. Here, however, we explore an alternative prior--the Beta-Liouville distribution--which offers a more flexible correlation structure than the Dirichlet. We examine the theoretical properties of the Beta-Liouville distribution, focusing on its conjugacy with the Multinomial likelihood. This property enables the derivation of update equations for a CAVI (Coordinate Ascent Variational Inference) variational algorithm, facilitating the approximate posterior estimation of model parameters. Additionally, we propose a stochastic variant of the CAVI algorithm that enhances scalability. The paper concludes with data examples that demonstrate effective strategies for setting the Beta-Liouville hyperparameters.