Wednesday, November 10, 2021

UQSay #37

The thirty-seventh UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, November 18, 2021.

2–3 PM — Toni Karvonen (University of Helsinki) — [slides]

Parameter estimation in Gaussian process regression for deterministic functions

In fields such as kriging, modelling of computer experiments, and probabilistic numerical computation, Gaussian process (GP) regression is used to interpolate deterministic functions which are observed without noise on compact sets. This talk reviews recent theoretical work on estimation of parameters (in particular via maximum likelihood) of the covariance kernel of the GP prior in such a setting, as well as the effect parameter estimation has on uncertainty quantification under model misspecification. We also discuss results on sample path properties of GPs that we use to characterise data-generating functions which resemble samples from a GP and to highlight the difference in assuming that the data are generated by some deterministic function or by a stochastic process. The results are based on the theory of reproducing kernel Hilbert spaces and function approximation in Sobolev spaces, which are briefly reviewed.

Ref: DOI:10.1137/20M1315968, arXiv:2103.03169, arXiv:2110.02810.

Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Didier Clouteau (MSSMAT), Amélie Fau (LMT), Filippo Gatti (MSSMAT), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (DOTA), Fernando Lopez-Caballero (MSSMAT), Didier Lucor (LISN), Emmanuel Vazquez (L2S).

Coordinator: Julien Bect (L2S).

Practical details: the seminar will be held online using Microsoft Teams.

If you want to attend this seminar (or any of the forthcoming online UQSay seminars), and if you do not already have access to the UQSay group on Teams, simply send an email and you will be invited. Please specify which email address the invitation must be sent to (this has to be the address associated with your Teams account).

You will find the link to the seminar on the "General" UQSay channel on Teams, approximately 15 minutes before the beginning.

The technical side of things: you can use Teams either directly from your web browser or using the "fat client", which is available for most platforms (Windows, Linux, Mac, Android & iOS). We strongly recommend the latter option whenever possible. Please give it a try before the seminar to anticipate potential problems.