Extended variational inference for Dirichlet process mixture of Beta-Liouville distributions for proportional data modeling

Abstract

Bayesian estimation of parameters in the Dirichlet mixture process of the Beta-Liouville distribution (i.e., the infinite Beta-Liouville mixture model) has recently gained considerable attention due to its modeling capability for proportional data. However, applying the conventional variational inference (VI) framework cannot derive an analytically tractable solution since the variational objective function cannot be explicitly calculated. In this paper, we adopt the recently proposed extended VI framework to derive the closed-form solution by further lower bounding the original variational objective function in the VI framework. This method is capable of simultaneously determining the model's complexity and estimating the model's parameters. Moreover, due to the nature of Bayesian nonparametric approaches, it can also avoid the problems of underfitting and overfitting. Extensive experiments were conducted on both synthetic and real data, generated from two real-world challenging applications, namely, object detection and text categorization, and its superior performance and effectiveness of the proposed method have been demonstrated.