# Compositionally-Warped Gaussian Processes

## TL;DR

The paper introduces the compositionally-warped Gaussian process (CWGP), a flexible, computationally efficient non-Gaussian model that improves prediction accuracy by using explicit inverse warping functions.

## Contribution

It proposes a novel class of warpings with known explicit inverse functions, enabling efficient deep compositional Gaussian processes.

## Key findings

- CWGP outperforms traditional warped GPs in prediction accuracy.
- CWGP offers shorter computation times compared to existing methods.
- Experimental results demonstrate robustness and improved model quality.

## Abstract

The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model Gaussian marginal distributions. To model non-Gaussian data, a GP can be warped by a nonlinear transformation (or warping) as performed by warped GPs (WGPs) and more computationally-demanding alternatives such as Bayesian WGPs and deep GPs. However, the WGP requires a numerical approximation of the inverse warping for prediction, which increases the computational complexity in practice. To sidestep this issue, we construct a novel class of warpings consisting of compositions of multiple elementary functions, for which the inverse is known explicitly. We then propose the compositionally-warped GP (CWGP), a non-Gaussian generative model whose expressiveness follows from its deep compositional architecture, and its computational efficiency is guaranteed by the analytical inverse warping. Experimental validation using synthetic and real-world datasets confirms that the proposed CWGP is robust to the choice of warpings and provides more accurate point predictions, better trained models and shorter computation times than WGP.