The seventy-eighth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, November 14, 2024.
2–3 PM — Botond Szabo (Bocconi University, Department of Decision Sciences - BIDSA) — [slides]
Uncertainty quantification and estimation with variational Gaussian Processes
We study the theoretical properties of a variational Bayes method in the Gaussian Process regression model. We consider the inducing variables method introduced by Titsias (2009b) and derive sufficient conditions for obtaining contraction rates for the corresponding variational Bayes (VB) posterior. We also derive guarantees and limitations for the associated credible sets. The derived general results are then applied for several specific examples. Finally, we also consider approximation methods from probabilistic numerics (e.g. Lanczos iteration and conjugate gradient descent). We demonstrate their close relationship with the variational Bayes approach and provide guidelines for these approaches as well to obtain optimal (minimax) statistical inference.
References:
- Contraction rates for sparse variational approximations in Gaussian process regression, 2022
- Uncertainty quantification for sparse spectral variational approximations in Gaussian process regression, 2023
- Contraction rates for conjugate gradient and Lanczos approximate posteriors in Gaussian process regression, 2024
Joint work with H. van Zanten (Vrije Universiteit Amsterdam) & D. Nieman (Vrije Universiteit Amsterdam) & B. Stankewitz (University of Potsdam).
Organizing committee: Pierre Barbillon (MIA-Paris), Julien Bect (L2S), Nicolas Bousquet (EDF R&D), Vincent Chabridon (EDF R&D), Amélie Fau (LMPS), Filippo Gatti (LMPS), Clément Gauchy (CEA), Bertrand Iooss (EDF R&D), Alexandre Janon (LMO), Sidonie Lefebvre (ONERA), Didier Lucor (LISN), Sébastien Petit (LNE), Emmanuel Vazquez (L2S), Xujia Zhu (L2S).
Coordinators: Sidonie Lefebvre (ONERA) & Xujia Zhu (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.
