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Variational Inference for Watson Mixture Model
KTH, School of Electrical Engineering (EES), Communication Theory.
KTH, School of Electrical Engineering (EES).
2016 (English)In: IEEE Transaction on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, E-ISSN 1939-3539, Vol. 38, no 9, 1886-1900 p.Article in journal (Refereed) Published
Abstract [en]

This paper addresses modelling data using the Watson distribution. The Watson distribution is one of the simplest distributions for analyzing axially symmetric data. This distribution has gained some attention in recent years due to its modeling capability. However, its Bayesian inference is fairly understudied due to difficulty in handling the normalization factor. Recent development of Markov chain Monte Carlo (MCMC) sampling methods can be applied for this purpose. However, these methods can be prohibitively slow for practical applications. A deterministic alternative is provided by variational methods that convert inference problems into optimization problems. In this paper, we present a variational inference for Watson mixture models. First, the variational framework is used to side-step the intractability arising from the coupling of latent states and parameters. Second, the variational free energy is further lower bounded in order to avoid intractable moment computation. The proposed approach provides a lower bound on the log marginal likelihood and retains distributional information over all parameters. Moreover, we show that it can regulate its own complexity by pruning unnecessary mixture components while avoiding over-fitting. We discuss potential applications of the modeling with Watson distributions in the problem of blind source separation, and clustering gene expression data sets.

Place, publisher, year, edition, pages
IEEE Computer Society, 2016. Vol. 38, no 9, 1886-1900 p.
Keyword [en]
Bayesian inference, variational inference, Watson distribution, mixture model, axially symmetric, clustering on the unit hypersphere, blind source separation, gene expression
National Category
Computer Systems
URN: urn:nbn:se:kth:diva-193190DOI: 10.1109/TPAMI.2015.2498935ISI: 000381432700013PubMedID: 26571512ScopusID: 2-s2.0-84981276074OAI: diva2:1034638

QC 20161012

Available from: 2016-10-12 Created: 2016-09-30 Last updated: 2016-10-12Bibliographically approved

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Taghia, JalilLeijon, Arne
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Communication TheorySchool of Electrical Engineering (EES)
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