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Conference Paper

Data modeling with the elliptical gamma distribution

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Sra, S., Hosseini, R., Theis, L., & Bethge, M. (2015). Data modeling with the elliptical gamma distribution. In G. Lebanon, & S. Vishwanathan (Eds.), Artificial Intelligence and Statistics, 9-12 May 2015, San Diego, California, USA (pp. 903-911). Madison, WI, USA: International Machine Learning Society.

Cite as: http://hdl.handle.net/11858/00-001M-0000-002A-4671-B
We study mixture modeling using the elliptical gamma (EG) distribution, a non-Gaussian distribution that allows heavy and light tail and peak behaviors. We first consider maximum likelihood parameter estimation, a task that turns out to be very challenging: we must handle positive definiteness constraints, and more crucially, we must handle possibly nonconcave log-likelihoods, which makes maximization hard. We overcome these difficulties by developing algorithms based on fixed-point theory; our methods respect the psd constraint, while also efficiently solving the (possibly) nonconcave maximization to global optimality. Subsequently, we focus on mixture modeling using EG distributions: we present a closed-form expression of the KL-divergence between two EG distributions, which we then combine with our ML estimation methods to obtain an efficient split-and-merge expectation maximization algorithm. We illustrate the use of our model and algorithms on a dataset of natural image patches.