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 to the unsupervised classification of short text data. While the Multinomial probability vector is traditionally assigned a Dirichlet prior distribution, this work explores an alternative formulation based on the Beta-Liouville distribution, which offers a more flexible correlation structure than the Dirichlet. We examine the theoretical properties of the Beta-Liouville distribution, with particular focus on its conjugacy with the Multinomial likelihood. This property enables the derivation of update equations for a CAVI (Coordinate Ascent Variational Inference) algorithm, facilitating approximate posterior inference of the model parameters. In addition, we introduce a stochastic variant of the CAVI algorithm to enhance scalability. The paper concludes with empirical examples demonstrating effective strategies for selecting the Beta-Liouville hyperparameters.