Robust and Conjugate Gaussian Process Regression

TL;DR

This paper introduces a robust Gaussian process regression method that maintains closed-form solutions under non-ideal noise conditions, improving reliability and computational efficiency in practical applications.

Contribution

The authors propose RCGP, a robust and conjugate GP regression approach that preserves closed-form updates using generalized Bayesian inference, applicable across various settings.

Findings

RCGP achieves reliable uncertainty quantification in noisy environments.

Empirical results show RCGP outperforms traditional methods in Bayesian optimization.

RCGP maintains computational efficiency comparable to standard GPs.

Abstract

To enable closed form conditioning, a common assumption in Gaussian process (GP) regression is independent and identically distributed Gaussian observation noise. This strong and simplistic assumption is often violated in practice, which leads to unreliable inferences and uncertainty quantification. Unfortunately, existing methods for robustifying GPs break closed-form conditioning, which makes them less attractive to practitioners and significantly more computationally expensive. In this paper, we demonstrate how to perform provably robust and conjugate Gaussian process (RCGP) regression at virtually no additional cost using generalised Bayesian inference. RCGP is particularly versatile as it enables exact conjugate closed form updates in all settings where standard GPs admit them. To demonstrate its strong empirical performance, we deploy RCGP for problems ranging from Bayesian optimisation to sparse variational Gaussian processes.