Bayesian estimation of generalized Gamma mixture model based on variational EM algorithm

Highlights：

• We propose a VEM algorithm for the inference of the generalized Gamma mixture model (GMM) with all the closed-form update equations.

• The help function is used to approximate the lower bound of the variational objective function in GMM.

• With the proposed VEM algorithm, the effective number of components as well as all the other underlying parameters in GMM can be estimated automatically and simultaneously.

• The results reveal that the proposed inference method is more efficient than the standard EM algorithm.

• The experimental results show that the GMM is more appropriate for the asymmetric and heavy-tailed data than Gaussian mixture model.

摘要

•We propose a VEM algorithm for the inference of the generalized Gamma mixture model (GMM) with all the closed-form update equations.•The help function is used to approximate the lower bound of the variational objective function in GMM.•With the proposed VEM algorithm, the effective number of components as well as all the other underlying parameters in GMM can be estimated automatically and simultaneously.•The results reveal that the proposed inference method is more efficient than the standard EM algorithm.•The experimental results show that the GMM is more appropriate for the asymmetric and heavy-tailed data than Gaussian mixture model.

论文关键词：Finite mixture models,Generalized Gamma distribution,Variational expectation-maximization (VEM),Maximum likelihood estimation,Extended factorized approximation

论文评审过程：Received 16 August 2017, Revised 22 September 2018, Accepted 21 October 2018, Available online 22 October 2018, Version of Record 28 October 2018.