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：为获得闭式条件推断，高斯过程回归通常假设观测噪声服从独立同分布的高斯分布。这一强假设在实际应用中常被违反，导致不可靠的推断与不确定性量化。然而，现有鲁棒化高斯过程的方法会破坏闭式条件推断，降低其工程应用价值并显著增加计算开销。本文证明，通过广义贝叶斯推断，可在几乎不增加计算成本的前提下实现可验证鲁棒共轭高斯过程回归。RCGP具有特殊优势，能够在所有标准高斯过程可进行闭式共轭更新的场景中实现精确的共轭闭环更新。为展示其卓越的实证性能，我们将RCGP应用于从贝叶斯优化到稀疏变分高斯过程等系列问题。