# Compositionally-Warped Gaussian Processes

arXiv: https://arxiv.org/abs/1906.09665 · HTML: https://mlsanity.com/paper/1906.09665/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2019.

## Built on by (most cited first, 14 of 14)

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- [Efficient Transformed Gaussian Processes for Non-Stationary Dependent Multi-class Classification](https://mlsanity.com/paper/2205.15008/) (2022)
- [Recent Advances in Data-Driven Wireless Communication Using Gaussian Processes: A Comprehensive Survey](https://mlsanity.com/paper/2103.10134/) (2021)
- [Towards Flexibility and Interpretability of Gaussian Process State-Space Model](https://mlsanity.com/paper/2301.08843/) (2023)
- [B2EA: An Evolutionary Algorithm Assisted by Two Bayesian Optimization Modules for Neural Architecture Search](https://mlsanity.com/paper/2202.03005/) (2022)
- [Towards Efficient Modeling and Inference in Multi-Dimensional Gaussian Process State-Space Models](https://mlsanity.com/paper/2309.01074/) (2023)
- [State-space deep Gaussian processes with applications](https://mlsanity.com/paper/2111.12604/) (2021)
- [Efficient Transformed Gaussian Process State-Space Models for Non-Stationary High-Dimensional Dynamical Systems](https://mlsanity.com/paper/2503.18309/) (2025)
- [Deep Transformed Gaussian Processes](https://mlsanity.com/paper/2310.18230/) (2023)
- [Variational Elliptical Processes](https://mlsanity.com/paper/2311.12566/) (2023)
- [To which reference class do you belong? Measuring racial fairness of reference classes with normative modeling](https://mlsanity.com/paper/2407.19114/) (2024)
- [Scalable Bayesian Transformed Gaussian Processes](https://mlsanity.com/paper/2210.10973/) (2022)
- [Monte Carlo inference for semiparametric Bayesian regression](https://mlsanity.com/paper/2306.05498/) (2023)

## Abstract (arXiv)

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.