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

arXiv: https://arxiv.org/abs/2003.07201 · HTML: https://mlsanity.com/paper/2003.07201/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2020.

## Built on by (most cited first, 1 of 1)

- [Sparse Variational Student-t Processes](https://mlsanity.com/paper/2312.05568/) (2023)

## Abstract (arXiv)

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.