# Chained Gaussian Processes

arXiv: https://arxiv.org/abs/1604.05263 · HTML: https://mlsanity.com/paper/1604.05263/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Apr 2016.

## Built on by (most cited first, 7 of 7)

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- [Detecting Label Noise via Leave-One-Out Cross-Validation](https://mlsanity.com/paper/2103.11352/) (2021)
- [Modular Gaussian Processes for Transfer Learning](https://mlsanity.com/paper/2110.13515/) (2021)
- [Gearing Gaussian process modeling and sequential design towards stochastic simulators](https://mlsanity.com/paper/2412.07306/) (2024)
- [Refined climatologies of future precipitation over High Mountain Asia using probabilistic ensemble learning](https://mlsanity.com/paper/2501.15690/) (2025)
- [Covariance-Boosted Gaussian Processes for Spatiotemporal Irregularities](https://mlsanity.com/paper/2607.23018/) (2026)

## Abstract (arXiv)

Gaussian process models are flexible, Bayesian non-parametric approaches to regression. Properties of multivariate Gaussians mean that they can be combined linearly in the manner of additive models and via a link function (like in generalized linear models) to handle non-Gaussian data. However, the link function formalism is restrictive, link functions are always invertible and must convert a parameter of interest to a linear combination of the underlying processes. There are many likelihoods and models where a non-linear combination is more appropriate. We term these more general models Chained Gaussian Processes: the transformation of the GPs to the likelihood parameters will not generally be invertible, and that implies that linearisation would only be possible with multiple (localized) links, i.e. a chain. We develop an approximate inference procedure for Chained GPs that is scalable and applicable to any factorized likelihood. We demonstrate the approximation on a range of likelihood functions.