Calibrated Computation-Aware Gaussian Processes
This work improves uncertainty quantification for large-scale regression problems using Gaussian processes, but it is incremental as it builds on existing CAGP frameworks.
The paper addresses the issue of conservative uncertainty quantification in computation-aware Gaussian processes (CAGPs) by proving that using a calibrated probabilistic linear solver ensures calibration in CAGPs, and proposes CAGP-GS based on Gauss-Seidel iterations, which performs well in low-dimensional test sets with few iterations.
Gaussian processes are notorious for scaling cubically with the size of the training set, preventing application to very large regression problems. Computation-aware Gaussian processes (CAGPs) tackle this scaling issue by exploiting probabilistic linear solvers to reduce complexity, widening the posterior with additional computational uncertainty due to reduced computation. However, the most commonly used CAGP framework results in (sometimes dramatically) conservative uncertainty quantification, making the posterior unrealistic in practice. In this work, we prove that if the utilised probabilistic linear solver is calibrated, in a rigorous statistical sense, then so too is the induced CAGP. We thus propose a new CAGP framework, CAGP-GS, based on using Gauss-Seidel iterations for the underlying probabilistic linear solver. CAGP-GS performs favourably compared to existing approaches when the test set is low-dimensional and few iterations are performed. We test the calibratedness on a synthetic problem, and compare the performance to existing approaches on a large-scale global temperature regression problem.