Bayesian Estimation of the von-Mises Fisher Mixture Model with Variational Inference
- 14 February 2014
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Pattern Analysis and Machine Intelligence
- Vol. 36 (9), 1701-1715
- https://doi.org/10.1109/tpami.2014.2306426
Abstract
This paper addresses the Bayesian estimation of the von-Mises Fisher (vMF) mixture model with variational inference (VI). The learning task in VI consists of optimization of the variational posterior distribution. However, the exact solution by VI does not lead to an analytically tractable solution due to the evaluation of intractable moments involving functional forms of the Bessel function in their arguments. To derive a closed-form solution, we further lower bound the evidence lower bound where the bound is tight at one point in the parameter distribution. While having the value of the bound guaranteed to increase during maximization, we derive an analytically tractable approximation to the posterior distribution which has the same functional form as the assigned prior distribution. The proposed algorithm requires no iterative numerical calculation in the re-estimation procedure, and it can potentially determine the model complexity and avoid the over-fitting problem associated with conventional approaches based on the expectation maximization. Moreover, we derive an analytically tractable approximation to the predictive density of the Bayesian mixture model of vMF distributions. The performance of the proposed approach is verified by experiments with both synthetic and real data.Keywords
This publication has 27 references indexed in Scilit:
- Digital Speech TransmissionPublished by Wiley ,2006
- A Bayesian Analysis of Directional Data Using the von Mises–Fisher DistributionCommunications in Statistics - Simulation and Computation, 2005
- 10.1162/jmlr.2003.4.6.1001Applied Physics Letters, 2000
- A full bayesian analysis of circular data using the von mises distributionThe Canadian Journal of Statistics / La Revue Canadienne de Statistique, 1999
- Comprehensive Identification of Cell Cycle–regulated Genes of the YeastSaccharomyces cerevisiaeby Microarray HybridizationMolecular Biology of the Cell, 1998
- Speaker recognition: A tutorialProceedings of the IEEE, 1997
- Simulation of the von mises fisher distributionCommunications in Statistics - Simulation and Computation, 1994
- Laplace approximations to posterior moments and marginal distributions on circles, spheres, and cylindersThe Canadian Journal of Statistics / La Revue Canadienne de Statistique, 1991
- Finding the Location of a Signal: A Bayesian AnalysisJournal of the American Statistical Association, 1988
- Bayesian inference for the von Mises-Fisher distributionBiometrika, 1976