Inference and Mixture Modeling with the Elliptical Gamma Distribution

TL;DR

This paper introduces efficient fixed-point algorithms for maximum likelihood estimation of the Elliptical Gamma Distribution and its mixtures, demonstrating their effectiveness in modeling natural image statistics with superior simplicity.

Contribution

Develops novel fixed-point algorithms for EGD ML estimation that are faster and more effective than existing methods, enabling practical mixture modeling.

Findings

Algorithms converge to global optima despite nonconvexity

EGD mixture models outperform competing approaches in natural image modeling

Proposed methods are significantly faster than previous algorithms

Abstract

We study modeling and inference with the Elliptical Gamma Distribution (EGD). We consider maximum likelihood (ML) estimation for EGD scatter matrices, a task for which we develop new fixed-point algorithms. Our algorithms are efficient and converge to global optima despite nonconvexity. Moreover, they turn out to be much faster than both a well-known iterative algorithm of Kent & Tyler (1991) and sophisticated manifold optimization algorithms. Subsequently, we invoke our ML algorithms as subroutines for estimating parameters of a mixture of EGDs. We illustrate our methods by applying them to model natural image statistics---the proposed EGD mixture model yields the most parsimonious model among several competing approaches.