Thursday, February 1, 2024

UQSay #69

The sixty-ninth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, February 8, 2024.

2–3 PM — Marouane Il Idrissi (EDF R&D - IMT) — [slides]

Generalized Hoeffding decomposition and the linear nature of non-linearity

Hoeffding’s decomposition of random outputs traditionally requires the inputs to be mutually independent. It allows uniquely decomposing a square-integrable function as a sum taken over every subset of inputs. Generalizing this result to non-mutually independent inputs has been a recent challenge in the literature on sensitivity analysis. Proposed solutions exist, but they require relatively restrictive assumptions on the distribution of the inputs. However, Hoeffding’s decomposition can be generalized under two reasonable assumptions on the inputs’ distribution: non-perfect functional dependence and non-degenerate stochastic dependence.

This generalization requires approaching the problem using a framework at the cornerstone of probability theory, functional analysis, and combinatorics. From this perspective, it can be seen as finding a direct-sum decomposition of a particular Lebesgue space, unveiling a surprisingly linear approach to handling stochastic and functional non-linearities. The proposed "ortho-canonical decomposition" relies on oblique projections rather than the traditional conditional expectations. Ultimately, it allows the definition of intuitive and interpretable sensitivity indices, which offers a path toward a more precise uncertainty quantification.

In this talk, we will delve into the unconventional framework used, discuss its nuances, and explore the various perspectives and challenges it offers.

Reference: Understanding black-box models with dependent inputs through a generalization of Hoeffding's decomposition, 2023 [github].

Joint work with Nicolas Bousquet (EDF R&D - LPSM), Fabrice Gamboa (IMT), Bertrand Ioss (EDF R&D - IMT) and Jean-Michel Loubes (IMT).

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.