Robust and Computation-Aware Gaussian Processes
Sinaga, Marshal, Martinelli, Julien, and Kaski, Samuel
Advances in neural information processing systems 39 (NeurIPS 2025) 2025
Gaussian processes (GPs) are widely used for regression and optimization tasks
such as Bayesian optimization (BO) due to their expressiveness and principled
uncertainty estimates. However, in settings with large datasets corrupted by outliers,
standard GPs and their sparse approximations struggle with computational tractability and robustness. We introduce Robust Computation-aware Gaussian Process
(RCaGP), a novel GP model that jointly addresses these challenges by combining a
principled treatment of approximation-induced uncertainty with robust generalized
Bayesian updating. The key insight is that robustness and approximation-awareness
are not orthogonal but intertwined: approximations can exacerbate the impact of
outliers, and mitigating one without the other is insufficient. Unlike previous
work that focuses narrowly on either robustness or approximation quality, RCaGP
combines both in a principled and scalable framework, thus effectively managing
both outliers and computational uncertainties introduced by approximations such
as low-rank matrix multiplications. Our model ensures more conservative and
reliable uncertainty estimates, a property we rigorously demonstrate. Additionally, we establish a robustness property and show that the mean function is key
to preserving it, motivating a tailored model selection scheme for robust mean
functions. Empirical results confirm that solving these challenges jointly leads to
superior performance across both clean and outlier-contaminated settings, both on
regression and high-throughput Bayesian optimization benchmarks.