Statistical inference with the Elliptical Gamma Distribution

Hosseini, R; Sra, S; Theis, L; Bethge, M

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Statistical inference with the Elliptical Gamma Distribution

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https://www.sciencedirect.com/science/article/pii/S0167947316300251
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Hosseini, R., Sra, S., Theis, L., & Bethge, M. (2016). Statistical inference with the Elliptical Gamma Distribution. Computational Statistics & Data Analysis, 101, 29-43.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0027-7FC9-2

Abstract

This paper studies mixture modeling using the Elliptical Gamma distribution (EGD)---a distribution that has parametrized tail and peak behaviors and offers richer modeling power than the multivariate Gaussian. First, we study maximum likelihood (ML) parameter estimation for a single EGD, a task that involves nontrivial conic optimization problems. We solve these problems by developing globally convergent fixed-point methods for them. Next, we consider fitting mixtures of EGDs, for which we first derive a closed-form expression for the KL-divergence between two EGDs and then use it in a ''split-and-merge'' expectation maximization algorithm. We demonstrate the ability of our proposed mixture modelling in modelling natural image patches.