Bayesian estimation of Dirichlet mixture model with variational inference
2014 (English)In: Pattern Recognition, ISSN 0031-3203, E-ISSN 1873-5142, Vol. 47, no 9, 3143-3157 p.Article in journal (Refereed) Published
In statistical modeling, parameter estimation is an essential and challengeable task. Estimation of the parameters in the Dirichlet mixture model (DMM) is analytically intractable, due to the integral expressions of the gamma function and its corresponding derivatives. We introduce a Bayesian estimation strategy to estimate the posterior distribution of the parameters in DMM. By assuming the gamma distribution as the prior to each parameter, we approximate both the prior and the posterior distribution of the parameters with a product of several mutually independent gamma distributions. The extended factorized approximation method is applied to introduce a single lower-bound to the variational objective function and an analytically tractable estimation solution is derived. Moreover, there is only one function that is maximized during iterations and, therefore, the convergence of the proposed algorithm is theoretically guaranteed. With synthesized data, the proposed method shows the advantages over the EM-based method and the previously proposed Bayesian estimation method. With two important multimedia signal processing applications, the good performance of the proposed Bayesian estimation method is demonstrated.
Place, publisher, year, edition, pages
2014. Vol. 47, no 9, 3143-3157 p.
Bayesian estimation, Variational inference, Extended factorized approximation, Relative convexity, Dirichlet distribution, Gamma prior, Mixture modeling, LSF quantization, Multiview depth image enhancement
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:kth:diva-147714DOI: 10.1016/j.patcog.2014.04.002ISI: 000336872000028ScopusID: 2-s2.0-84900821630OAI: oai:DiVA.org:kth-147714DiVA: diva2:732938
QC 201407072014-07-072014-07-032014-07-07Bibliographically approved