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

Comparative Analysis of Improved Dirichlet Process Mixture Model

“…This means that different indicators can follow different distributions, enabling its direct application in the clustering of multi-source data and addressing the related issues in multi-source data clustering. Lai et al [12] used the stick-breaking construction of the Dirichlet process as the prior distribution of the mixture weights in Gaussian mixture models, establishing the Dirichlet process mixture model and using variational methods to estimate the model parameters. The results showed that this method achieved better performance than traditional kernel principal component analysis.…”