Unsupervised sentiment detection with mixtures of Beta-Liouville Multinomial distributions

In this paper, we present a fully Bayesian Beta-Liouville Multinomial mixture model for unsupervised sentiment identification. The Beta-Liouville distribution has recently emerged as a flexible and powerful alternative to the Dirichlet prior in statistical language modeling. While maintaining conjugacy with the Multinomial likelihood, it introduces an additional shape parameter that allows for a more expressive and adaptable covariance structure. For posterior inference, we develop a coordinate ascent variational algorithm that maximizes an analytically tractable lower bound on the marginal likelihood with respect to a set of variational parameters. Crucially, the model is reparameterized so that the Dirichlet-Multinomial mixture appears as a special case of the more general Beta-Liouville formulation, thus providing a unified and versatile probabilistic framework. The proposed methodology is empirically assessed on benchmark datasets involving binary and ternary sentiment classification, as well as irony detection, highlighting its enhanced flexibility in modeling emotional polarity in ultra-short textual data.