Statistical inference with the Elliptical Gamma Distribution

This paper studies mixture modeling using the Elliptical Gamma distribution (EGD)—a distri-bution 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 devel-oping 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