Bayesian Estimation of Beta Mixture Models with Variational Inference
2011 (English)In: IEEE Transaction on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, Vol. 33, no 11, 2160-2173 p.Article in journal (Refereed) Published
Bayesian estimation of the parameters in beta mixture models (BMM) is analytically intractable. The numerical solutionsto simulate the posterior distribution are available, but incur high computational cost. In this paper, we introduce an approximation tothe prior/posterior distribution of the parameters in the beta distribution and propose an analytically tractable (closed-form) Bayesianapproach to the parameter estimation. The approach is based on the variational inference (VI) framework. Following the principles ofthe VI framework and utilizing the relative convexity bound, the extended factorized approximation method is applied to approximate thedistribution of the parameters in BMM. In a fully Bayesian model where all the parameters of the BMM are considered as variables andassigned proper distributions, our approach can asymptotically find the optimal estimate of the parameters posterior distribution. Also,the model complexity can be determined based on the data. The closed-form solution is proposed so that no iterative numericalcalculation is required. Meanwhile, our approach avoids the drawback of overfitting in the conventional expectation maximizationalgorithm. The good performance of this approach is verified by experiments with both synthetic and real data.
Place, publisher, year, edition, pages
2011. Vol. 33, no 11, 2160-2173 p.
Bayesian Estimation, Maximum Likelihood Estimation, Beta Distribution, Mixture Modeling, Variational Inference, Factorized Approximation
Computer and Information Science
Research subject SRA - ICT
IdentifiersURN: urn:nbn:se:kth:diva-33677DOI: 10.1109/TPAMI.2011.63ISI: 000294910000004ScopusID: 2-s2.0-80053127168OAI: oai:DiVA.org:kth-33677DiVA: diva2:416992
QC 201109292011-05-162011-05-132011-11-15Bibliographically approved