Inference and Mixture Modeling with the Elliptical Gamma Distribution
This work addresses the challenge of efficient inference for a specific statistical distribution, which is incremental as it improves upon existing algorithms for EGD modeling.
The authors tackled the problem of parameter estimation for the Elliptical Gamma Distribution (EGD) and its mixtures by developing new fixed-point algorithms for maximum likelihood estimation, which are efficient, converge to global optima, and are much faster than existing methods. They applied these methods to model natural image statistics, achieving the most parsimonious model among competing approaches.
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.