Computation-Aware Robust Gaussian Processes

Abstract

Gaussian Processes (GPs) are flexible nonparametric statistical models equipped with principled uncertainty quantification for both noise and model uncertainty. However, their cubic inference complexity requires them to be combined with approximation techniques when applied to large datasets. Recent work demonstrated that such approximations introduce an additional source of uncertainty, computational uncertainty, and that the latter could be quantified, leading to the computation-aware GP, also known as IterGP. In this short communication, we demonstrate that IterGP is not "robust", in the sense that a quantity of interest, the posterior influence function, is not bounded. Subsequently, drawing inspiration from recent work on Robust Conjugate GPs, we introduce a novel class of GPs: IterRCGPs. We carry out a number of theoretical analyses, demonstrating the robustness of IterRCGPs among other things.