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Inference and mixture modeling with the Elliptical Gamma Distribution

Author

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  • Hosseini, Reshad
  • Sra, Suvrit
  • Theis, Lucas
  • Bethge, Matthias

Abstract

The authors study modeling and inference with the Elliptical Gamma Distribution (EGD). In particular, Maximum likelihood (ML) estimation for EGD scatter matrices is considered, a task for which the authors present new fixed-point algorithms. The algorithms are shown to be efficient and convergent to global optima despite non-convexity. Moreover, they turn out to be much faster than both a well-known iterative algorithm of Kent & Tyler and sophisticated manifold optimization algorithms. Subsequently, the ML algorithms are invoked as subroutines for estimating parameters of a mixture of EGDs. The performance of the methods is illustrated on the task of modeling natural image statistics—the proposed EGD mixture model yields the most parsimonious model among several competing approaches.

Suggested Citation

  • Hosseini, Reshad & Sra, Suvrit & Theis, Lucas & Bethge, Matthias, 2016. "Inference and mixture modeling with the Elliptical Gamma Distribution," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 29-43.
    • Handle: RePEc:eee:csdana:v:101:y:2016:i:c:p:29-43
    DOI: 10.1016/j.csda.2016.02.009
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    References listed on IDEAS

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    1. Arellano-Valle, R.B. & del Pino, G. & Iglesias, P., 2006. "Bayesian inference in spherical linear models: robustness and conjugate analysis," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 179-197, January.
    2. Lin, Tsung-I & McNicholas, Paul D. & Ho, Hsiu J., 2014. "Capturing patterns via parsimonious t mixture models," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 80-87.
    3. Dümbgen, Lutz & Nordhausen, Klaus & Schuhmacher, Heike, 2016. "New algorithms for M-estimation of multivariate scatter and location," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 200-217.
    4. N. H. Bingham & Rudiger Kiesel, 2002. "Semi-parametric modelling in finance: theoretical foundations," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 241-250.
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