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  Data modeling with the elliptical gamma distribution

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.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-4671-B Version Permalink: http://hdl.handle.net/21.11116/0000-0001-ACA2-6
Genre: Conference Paper

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 Creators:
Sra, S, Author              
Hosseini, R, Author              
Theis, L1, Author              
Bethge, M1, Author              
Affiliations:
1Werner Reichardt Centre for Integrative Neuroscience, Tübingen, ou_persistent22              

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 Abstract: 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.

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 Dates: 2015-05
 Publication Status: Published in print
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 Identifiers: BibTex Citekey: SraHTB2015
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Title: 18th International Conference on Artificial Intelligence and Statistics (AISTATS 2015)
Place of Event: San Diego, CA, USA
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Title: Artificial Intelligence and Statistics, 9-12 May 2015, San Diego, California, USA
Source Genre: Proceedings
 Creator(s):
Lebanon, G, Editor
Vishwanathan, SVN, Editor
Affiliations:
-
Publ. Info: Madison, WI, USA : International Machine Learning Society
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 903 - 911 Identifier: -

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Title: JMLR Workshop and Conference Proceedings
Source Genre: Series
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Pages: - Volume / Issue: 38 Sequence Number: - Start / End Page: - Identifier: -