Institute of Mathematical Statistics and Actuarial Science

Swiss Statistics Seminar

Friday, March 24, 2023

Lecture room B6
Institute for Exact Sciences
Sidlerstr. 5
CH-3012 Bern


14:30-15:30 h

On Gaussian Process Multiple-Fold Cross-Validation

David Ginsbourger (University of Bern)

In this talk I will give an overview of some recent results pertaining to Gaussian Process multiple-fold cross-validation. In the first part, the focus will be put on results from (arXiv:2101.03108, joint work with Cedric Schärer), where block inversion is employed to efficiently calculate multiple-fold cross-validation residuals and their covariances. I will discuss implications of the resulting cross-validation covariance structure on model diagnostics and also how its knowledge helps clarifying some connections between cross-validation-based parameter estimation and MLE.

In the second part I will focus on the impact of grouping the observations, referred to as "fold design", on the estimation of kernel hyperparameters. In particular, numerical results from a joint work with Athénaïs Gautier and Cédric Travelletti on an inverse problem from geosciences will be used to illustrate how the way of designing folds may affect the estimation of a correlation length of interest.