# Variational Elliptical Processes

arXiv: https://arxiv.org/abs/2311.12566 · HTML: https://mlsanity.com/paper/2311.12566/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 74 references that are in the map.
- First posted on arXiv 21 Nov 2023.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Deep Kernel Learning](https://mlsanity.com/paper/1511.02222/) (2015)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Black Box Variational Inference](https://mlsanity.com/paper/1401.0118/) (2013)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [Noise Flow: Noise Modeling with Conditional Normalizing Flows](https://mlsanity.com/paper/1908.08453/) (2019)
- [Stochastic Variational Deep Kernel Learning](https://mlsanity.com/paper/1611.00336/) (2016)
- [Manifold Gaussian Processes for Regression](https://mlsanity.com/paper/1402.5876/) (2014)
- [Student-t Processes as Alternatives to Gaussian Processes](https://mlsanity.com/paper/1402.4306/) (2014)
- [Global inducing point variational posteriors for Bayesian neural networks and deep Gaussian processes](https://mlsanity.com/paper/2005.08140/) (2020)
- [Variational Implicit Processes](https://mlsanity.com/paper/1806.02390/) (2018)
- [Invertible Generative Modeling using Linear Rational Splines](https://mlsanity.com/paper/2001.05168/) (2020)
- [Automated Variational Inference in Probabilistic Programming](https://mlsanity.com/paper/1301.1299/) (2013)
- [Deep kernel processes](https://mlsanity.com/paper/2010.01590/) (2020)
- [The Variational Gaussian Process](https://mlsanity.com/paper/1511.06499/) (2015)
- [Transforming Gaussian Processes With Normalizing Flows](https://mlsanity.com/paper/2011.01596/) (2020)
- [The Scenario Approach for Stochastic Model Predictive Control with Bounds on Closed-Loop Constraint Violations](https://mlsanity.com/paper/1307.5640/) (2013)
- [Orthogonally Decoupled Variational Gaussian Processes](https://mlsanity.com/paper/1809.08820/) (2018)
- [Deep Gaussian Processes with Importance-Weighted Variational Inference](https://mlsanity.com/paper/1905.05435/) (2019)
- [Open Power System Data - Frictionless data for electricity system modelling](https://mlsanity.com/paper/1812.10405/) (2018)
- [Compositionally-Warped Gaussian Processes](https://mlsanity.com/paper/1906.09665/) (2019)

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

- [Sparse Variational Student-t Processes for Heavy-tailed Modeling](https://mlsanity.com/paper/2408.06699/) (2024)

## Abstract (arXiv)

We present elliptical processes, a family of non-parametric probabilistic models that subsume Gaussian processes and Student's t processes. This generalization includes a range of new heavy-tailed behaviors while retaining computational tractability. Elliptical processes are based on a representation of elliptical distributions as a continuous mixture of Gaussian distributions. We parameterize this mixture distribution as a spline normalizing flow, which we train using variational inference. The proposed form of the variational posterior enables a sparse variational elliptical process applicable to large-scale problems. We highlight advantages compared to Gaussian processes through regression and classification experiments. Elliptical processes can supersede Gaussian processes in several settings, including cases where the likelihood is non-Gaussian or when accurate tail modeling is essential.