Inference and mixture modeling with the Elliptical Gamma Distribution
| Autor: | Matthias Bethge, Suvrit Sra, Lucas Theis, Reshad Hosseini |
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| Rok vydání: | 2016 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Mathematical optimization Iterative method Subroutine Maximum likelihood Inference Machine Learning (stat.ML) 02 engineering and technology Statistics - Computation 01 natural sciences Image (mathematics) 010104 statistics & probability Statistics - Machine Learning FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Gamma distribution 0101 mathematics Mathematics - Optimization and Control Computation (stat.CO) Computer Science::Databases Mathematics Applied Mathematics Mixture model Computational Mathematics Task (computing) Computational Theory and Mathematics Optimization and Control (math.OC) 020201 artificial intelligence & image processing Algorithm |
| Zdroj: | Computational Statistics Data Analysis |
| ISSN: | 0167-9473 |
| Popis: | 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. 23 pages, 11 figures |
| Databáze: | OpenAIRE |
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