… Let us consider a dataset X and  ¼ fZ; ®; g as the set of random variables of innite MB
mixture model. In variational inference, our goal is to nd an approximation QðÂÞ for the true …

… Gaussian mixture models (… Beta mixture models which are developed based on a very
flexible distribution which does not have a constant shape and is appropriate to be used to model …

… framework, the focus of this article is on the Bayesian estimation of the IBMM using the SVI
framework. However, for the non-Gaussian statistical models, such as WMM, vFMM, BMM, …

… In this section, we extend conventional variational inference to online settings following
the framework in Reference 39. This method is a capable alternative to handle real-world …

… , non-Gaussian mixture models have been reported in the literature, including the mixtures
of the Beta … In what follows, we propose a Bayesian variational inference to overcome the …

… survey of the theoretical literature on variational inference until around 2017; we discuss …
the Gaussian mixture model and the latent Dirichlet allocation in Section 4. Observe that the …

… mixture model (InIDMM), 22 the infinite Beta-Liouville mixture model (InBLMM), 42 and
the infinite Beta mixture … , we focus on the Bayesian estimation of the DPM of Beta-Liouville …

… an extended variational inference method for the inverted Beta-Liouville mixture model, and
derives the analytical tractable solution of the optimization equations of the model. Second, …

… of inference using variational approximations. We show that, in a wide range of parametric
mixture models, … variational inference and M-estimation that we will use throughout this article. …

… the Bayesian estimation of the finite Gamma mixture model (… Moreover, the optimal
mixture component number can be … Beta mixture model (IBMM) [5], inverted Dirichlet mixture …