Numerical issues in maximum likelihood parameter estimation for Gaussian process interpolation

Abstract : This article investigates the origin of numerical issues in maximum likelihood parameter estimation for Gaussian process (GP) interpolation and investigates simple but effective strategies for improving commonly used open-source software implementations. This work targets a basic problem but a host of studies, particularly in the literature of Bayesian optimization, rely on off-the-shelf GP implementations. For the conclusions of these studies to be reliable and reproducible, robust GP implementations are critical.