Advancing Multinomial Regression and Topic Modeling with Beta-Liouville Distributions

This research explores the Beta-Liouville (BL) distribution as an alternative to the classic Dirichlet distribution in Dirichlet multinomial regression (DMR) and topic modelling. We examine the inherent limitations presented by the Dirichlet distribution in DMR, particularly in handling sparse data and complex correlations, then propose that the BL distribution, with its inherent flexibility and ability to handle higher-dimensional data, presents a substantial upgrade. We demonstrate the advantages of this new approach through a series of simulated and real-world datasets, highlighting improvements in model performance and inference quality. We discuss the impact of this change in the realm of topic modelling, as well as how the BL distribution enhances the interpretability and specificity of topics extracted. We anticipate our work to inspire further research and development in this field, aiming for continued refinement and enhancement of predictive modelling.