Bayesian estimation of beta mixture models with variational inference

IEEE Transactions on Pattern Analysis and Machine Intelligence
Zhanyu Ma, Arne Leijon

Abstract

Bayesian estimation of the parameters in beta mixture models (BMM) is analytically intractable. The numerical solutions to simulate the posterior distribution are available, but incur high computational cost. In this paper, we introduce an approximation to the prior/posterior distribution of the parameters in the beta distribution and propose an analytically tractable (closed form) Bayesian approach to the parameter estimation. The approach is based on the variational inference (VI) framework. Following the principles of the VI framework and utilizing the relative convexity bound, the extended factorized approximation method is applied to approximate the distribution of the parameters in BMM. In a fully Bayesian model where all of the parameters of the BMM are considered as variables and assigned 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 numerical calculation is required. Meanwhile, our approach avoids the drawback of overfitting in the conventional expectation maximization algorithm. The good performance of this approach is veri...Continue Reading

References

Nov 12, 2002·Neural Networks : the Official Journal of the International Neural Network Society·Naonori Ueda, Zoubin Ghahramani
May 27, 2003·Nature Reviews. Immunology·Ed Palmer
Feb 17, 2005·Bioinformatics·Yuan JiKevin R Coombes

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Citations

Jun 18, 2014·International Journal of Molecular Sciences·Zhanyu MaJun Guo
May 9, 2014·IEEE Transactions on Neural Networks and Learning Systems·Wentao Fan, Nizar Bouguila
May 1, 2012·IEEE Transactions on Neural Networks and Learning Systems·Wentao FanDjemel Ziou
Sep 10, 2015·IEEE Transactions on Pattern Analysis and Machine Intelligence·Jalil TaghiaArne Leijon
Sep 10, 2015·IEEE Transactions on Pattern Analysis and Machine Intelligence·Zhanyu MaJun Guo
Nov 17, 2015·IEEE Transactions on Pattern Analysis and Machine Intelligence·Jalil Taghia, Arne Leijon
Jul 19, 2013·Journal of Bioinformatics and Computational Biology·Zhanyu Ma, Andrew E Teschendorff
Oct 13, 2018·Bulletin of Mathematical Biology·Eduard Campillo-FunolletAnotida Madzvamuse
Sep 4, 2020·Nature Genetics·Giulio CaravagnaAndrea Sottoriva

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