Numerical issues in maximum likelihood parameter estimation for Gaussian process interpolation

Subhasish Basak (1) , Sébastien Petit (1) , Julien Bect (1, 2) , Emmanuel Vazquez (2, 1)

1 L2S - Laboratoire des signaux et systèmes
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

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.

Keywords: Gaussian process; Maximum likelihood estimation; Optimization

Domains: Statistics [stat]; Machine Learning [stat.ML]; Statistics [stat]; Computation [stat.CO]

Subhasish Basak, Sébastien Petit, Julien Bect, Emmanuel Vazquez. Numerical issues in maximum likelihood parameter estimation for Gaussian process interpolation. 7th International Conference on machine Learning, Optimization and Data science (LOD 2021), Oct 2021, Grasmere, United Kingdom. ⟨10.1007/978-3-030-95470-3_9⟩. ⟨hal-03119528v2⟩