# Non-Gaussian Process Regression

arXiv: https://arxiv.org/abs/2209.03117 · HTML: https://mlsanity.com/paper/2209.03117/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 58 references that are in the map.
- First posted on arXiv 7 Sep 2022.

## Builds on (most cited first, 10 of 10)

- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Input Warping for Bayesian Optimization of Non-stationary Functions](https://mlsanity.com/paper/1402.0929/) (2014)
- [Student-t Processes as Alternatives to Gaussian Processes](https://mlsanity.com/paper/1402.4306/) (2014)
- [Generalized Spectral Kernels](https://mlsanity.com/paper/1506.02236/) (2015)
- [Scalable L'evy Process Priors for Spectral Kernel Learning](https://mlsanity.com/paper/1802.00530/) (2018)
- [String and Membrane Gaussian Processes](https://mlsanity.com/paper/1507.06977/) (2015)
- [The L'evy State Space Model](https://mlsanity.com/paper/1912.12524/) (2019)
- [Modelling Non-Smooth Signals with Complex Spectral Structure](https://mlsanity.com/paper/2203.06997/) (2022)
- [Point process simulation of generalised inverse Gaussian processes and estimation of the Jaeger integral](https://mlsanity.com/paper/2105.09429/) (2021)

## Built on by (most cited first, 2 of 2)

- [Combining Bayesian Inference and Reinforcement Learning for Agent Decision Making: A Review](https://mlsanity.com/paper/2505.07911/) (2025)
- [Multifidelity-Augmented Gaussian Process Inputs for Surrogate Modeling from Scarce Data](https://mlsanity.com/paper/2603.22050/) (2026)

## Abstract (arXiv)

Standard GPs offer a flexible modelling tool for well-behaved processes. However, deviations from Gaussianity are expected to appear in real world datasets, with structural outliers and shocks routinely observed. In these cases GPs can fail to model uncertainty adequately and may over-smooth inferences. Here we extend the GP framework into a new class of time-changed GPs that allow for straightforward modelling of heavy-tailed non-Gaussian behaviours, while retaining a tractable conditional GP structure through an infinite mixture of non-homogeneous GPs representation. The conditional GP structure is obtained by conditioning the observations on a latent transformed input space and the random evolution of the latent transformation is modelled using a L'evy process which allows Bayesian inference in both the posterior predictive density and the latent transformation function. We present Markov chain Monte Carlo inference procedures for this model and demonstrate the potential benefits compared to a standard GP.