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

•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 compon...

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Vydáno v:	Pattern recognition Ročník 87; s. 269 - 284
Hlavní autoři:	Liu, Chi, Li, Heng-Chao, Fu, Kun, Zhang, Fan, Datcu, Mihai, Emery, William J.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Ltd 01.03.2019
Témata:	Extended factorized approximation Finite mixture models Generalized Gamma distribution Maximum likelihood estimation Variational expectation-maximization (VEM) Maximum likelihood estimation Finite mixture models Generalized Gamma distribution Extended factorized approximation Variational expectation-maximization (VEM)
ISSN:	0031-3203, 1873-5142
On-line přístup:	Získat plný text
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Popis
Shrnutí:	•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. In this paper, we propose a Bayesian inference method for the generalized Gamma mixture model (GΓMM) based on variational expectation-maximization algorithm. Specifically, the shape parameters, the inverse scale parameters, and the mixing coefficients in the GΓMM are treated as random variables, while the power parameters are left as parameters without assigning prior distributions. The help function is designed to approximate the lower bound of the variational objective function, which facilitates the assignment of the conjugate prior distributions and leads to the closed-form update equations. On this basis, the variational E-step and the variational M-step are alternatively implemented to infer the posteriors of the variables and estimate the parameters. The computational demand is reduced by the proposed method. More importantly, the effective number of components of the GΓMM can be determined automatically. The experimental results demonstrate the effectiveness of the proposed method especially in modeling the asymmetric and heavy-tailed data.
ISSN:	0031-3203 1873-5142
DOI:	10.1016/j.patcog.2018.10.025