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.

翻译：为实现闭式条件化，高斯过程（GP）回归中一个常见假设是观测噪声为独立同分布的高斯噪声。这一强假设且过于简化的条件在实践中常被违反，导致不可靠的推断与不确定性量化。遗憾的是，现有鲁棒化高斯过程的方法破坏了闭式条件化特性，使其对实践者吸引力降低且计算成本显著增加。本文通过广义贝叶斯推断，展示了如何以几乎无额外计算代价实现可证明的鲁棒共轭高斯过程（RCGP）回归。RCGP具有突出的通用性，能在所有标准高斯过程允许的场景中实现精确的共轭闭式更新。为验证其卓越的实证性能，我们将RCGP应用于从贝叶斯优化到稀疏变分高斯过程等一系列问题。