Bayesian Estimation of the von-Mises Fisher Mixture Model with Variational Inference

IEEE Transactions on Pattern Analysis and Machine Intelligence
Jalil TaghiaArne Leijon

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 v...Continue Reading

References

Dec 19, 2001·Neural Computation·Janne Sinkkonen, Samuel Kaski
Sep 12, 2003·Bioinformatics·Inderjit S DhillonUsman Roshan
Mar 23, 2011·IEEE Transactions on Pattern Analysis and Machine Intelligence·Zhanyu Ma, Arne Leijon

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Citations

Jun 18, 2014·International Journal of Molecular Sciences·Zhanyu MaJun Guo
Nov 17, 2015·IEEE Transactions on Pattern Analysis and Machine Intelligence·Jalil Taghia, Arne Leijon
Aug 5, 2017·Neural Computation·Rasmus E RøgeMorten Mørup
Aug 6, 2016·Molecular Informatics·Erik GawehnGisbert Schneider

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