Thursday, January 18, 2024

UQSay #68

The sixty-eighth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, January 25, 2024.

2–3 PM — Gabriel Sarazin (CEA Paris Saclay) — [slides]

Towards more interpretable kernel-based sensitivity analysis

When working with a computationally-expensive simulation code involving a large number of uncertain physical parameters, it is often advisable to perform a preliminary sensitivity analysis in order to identify which input variables will really be useful for surrogate modelling. On paper, the total-order Sobol' indices fulfill this role perfectly, since they are able to detect any type of input-output dependence, while being interpretable as simple percentages of the output variance. However, in many situations, their accurate estimation remains a thorny issue, despite remarkable progress in that direction over the past few months. In this context where inference is strongly constrained, kernel methods have emerged as an excellent alternative, notably through the Hilbert-Schmidt independence criterion (HSIC). Although they offer undeniable advantages over Sobol' indices, HSIC indices are much harder to understand, and this lack of interpretability is a major obstacle to their wider dissemination. In order to marry the advantages of Sobol' and HSIC indices, an ANOVA-like decomposition allows to define HSIC-ANOVA indices at all orders, just as would be done for Sobol' indices. This recent contribution is the starting point of this presentation.

The main objective of this talk is to provide deeper insights into the HSIC-ANOVA framework. One major difference with the basic HSIC framework lies in the use of specific input kernels (like Sobolev kernels). First, a dive into the universe of cross-covariance operators will allow to better understand how sensitivity is measured by HSIC-ANOVA indices, and what type of input-output dependence is captured by each term of the HSIC-ANOVA decomposition. Then, a brief study of Sobolev kernels, focusing more particularly on their feature maps, will reveal what kind of simulators are likely to elicit HSIC-ANOVA interactions. It will also be demonstrated that Sobolev kernels are characteristic, which ensures that HSIC-ANOVA indices can be used to test input-output independence. Finally, a test procedure will be proposed for the total-order HSIC-ANOVA index, and it will be shown (numerically) that the resulting test of independence is at least as powerful as the standard test (based on two Gaussian kernels).

Reference: New insights into the feature maps of Sobolev kernels: application in global sensitivity analysis, 2023 [sensiHSIC & testHSIC in R package sensitivity].

Joint work with Amandine Marrel (CEA Cadarache), Sébastien Da Veiga (ENSAI) and Vincent Chabridon (EDF R&D).

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

Coordinators: Julien Bect (L2S) & Sidonie Lefebvre (ONERA)

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.