The Elliptical Processes: a Family of Fat-tailed Stochastic Processes

• URL: http://arxiv.org/abs/2003.07201v2
• Date: Wed, 2 Dec 2020 07:27:47 GMT
• Title: The Elliptical Processes: a Family of Fat-tailed Stochastic Processes
• Authors: Maria B{\aa}nkestad, Jens Sj\"olund, Jalil Taghia, Thomas Sch\"on
• Abstract summary: We present the elliptical processes -- a family of non-parametric probabilistic models that subsumes the Gaussian process and the Student-t process. This generalization includes a range of new fat-tailed behaviors yet retains computational tractability.
• Score: 1.2043574473965317
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present the elliptical processes -- a family of non-parametric probabilistic models that subsumes the Gaussian process and the Student-t process. This generalization includes a range of new fat-tailed behaviors yet retains computational tractability. We base the elliptical processes on a representation of elliptical distributions as a continuous mixture of Gaussian distributions and derive closed-form expressions for the marginal and conditional distributions. We perform numerical experiments on robust regression using an elliptical process defined by a piecewise constant mixing distribution, and show advantages compared with a Gaussian process. The elliptical processes may become a replacement for Gaussian processes in several settings, including when the likelihood is not Gaussian or when accurate tail modeling is critical.

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