2020/03/13 by Maria Bånkestad, Bånkestad, Maria, Jens Sjölund +5
Economics, Econometrics and Finance · #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Methodology (stat.ME) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2003.07201
openalex publication_date 2020/03/13 · openalex created_date 2020/12/07 · openalex updated_date 2026/07/28
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.