UQSay # 84

The eighty-fourth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, March 6, 2025.

2–3 PM — Elena Di Bernardino (Laboratoire Jean Alexandre Dieudonné, Université Côte d'Azur) — [slides]

Curvature measures for random excursion sets: theoretical and computational developments

The excursion set of a smooth random field carries relevant information in its various geometric measures. Geometric properties of these exceedance regions above a given level provide meaningful theoretical and statistical characterizations for random fields defined on Euclidean domains. Many theoretical results have been obtained for excursions of Gaussian processes and include expected values of the so-called Lipschitz-Killing curvatures (LKCs), such as the area, perimeter and Euler characteristic in two-dimensional Euclidean space. In this talk we will describe a recent series of theoretical and computational contributions in this field. Our aim is to provide answers to questions like:

- How the geometric measures of an excursion set can be inferred from a discrete sample of the excursion set;

- How these measures can be related back to the distributional properties of the random field from which the excursion set was obtained;

- How the excursion set geometry can be used to infer the extremal behavior of random fields.

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.

UQSay #83

The eighty-third UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, February 13, 2025.

2–3 PM — Margot Hérin (LIP6, Sorbonne University) — [slides]

Algorithms for learning capacity-based preference models

Preference models from Decision Theory are used to describe, explain, or predict human behavior in evaluation or decision-making tasks. Beyond this descriptive role, a key feature of these models is their ability to guarantee normative properties, ensuring the internal consistency of the modeled value system and the resulting decisions. Hence, they can also be used to assist individuals in making a relevant choice based on their preferences or provide machines with the ability to autonomously yet controllably make sophisticated decisions in complex environments, involving multi-criteria or collective decision-making, or decision-making under uncertainty.

In this talk, we consider aggregation functions weighted by a non-additive set function (called capacity), such as multilinear utilities or Choquet integrals. The non-additivity of the capacity makes it possible to model criteria interactions, leaving room for a diversity of attitudes in criteria aggregation. However, allowing for these interactions dramatically increases the complexity of the preference learning task and may prevent the model from being interpretable, due to the combinatorial nature of the possible interactions.

We address this challenge by learning a sparse Möbius transform of the capacity, where the few non-zero Möbius masses indicate the significant positive or negative synergies between criteria. Specifically, we propose a learning method based on iterative reweighted least squares (IRLS) for sparse recovery, and dualization to improve scalability, making it possible to handle aggregation problems involving more than 20 criteria. We also present an online learning algorithm based on regularized dual averaging (RDA), designed for decision-making contexts where preference examples become available sequentially, but also well suited to handle large-scale preference databases (large number of preferences or criteria examples). In addition, the inclusion of normative constraints on the capacity (e.g., monotonicity, supermodularity) is made possible by combining RDA with the method of alternating direction multipliers (ADMM).

References:

• Learning Preference Models with Sparse Interactions of Criteria, IJCAI 2023
• Online Learning of Capacity-Based Preference Models, IJCAI 2024

Joint work with P. Perny (Sorbonne University) & N. Sokolovska (Sorbonne University).

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.

UQSay #82

The eighty-second UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, January 30, 2025.

2-3 PM — Alexandros A. Taflanidis (University of Notre Dame, Department of Civil and Environmental Engineering and Earth Sciences, USA) — [slides]

Reduced order and surrogate modeling applications for computationally efficient uncertainty propagation within seismic vulnerability assessment

Seismic vulnerability assessment involves the quantification and propagation of the different courses of uncertainty impacting structural performance. For engineering demand parameters (EDPs) the relevant uncertainties pertain to the seismic hazard and/or to the structural model characteristics, while the detailed characterization of structural vulnerability is typically performed using nonlinear response-history analysis (NLRHA). Despite recent advances in computational science, the adoption of computationally intensive, high-fidelity finite element models (FEMs) for performing NLRHA remains a challenge for many seismic risk assessment applications, forcing some sort of simplification of the uncertainty characterization. This presentation will investigate two alternative computational statistics approaches for improving computational efficiency in such settings.

The first approach will be the use of reduced order models (ROMs), coupled, if needed, with a Multi-Fidelity Monte Carlo (MFMC) implementation. ROMs simplify the physics-based description of the original FEM through some form of condensation of the degrees of freedom and equations of motion, coupled with an approximation of the nonlinear (hysteretic) response characteristics. In order to accommodate any potential bias from the ROM approximation, a MFMC setting is additionally examined. In the latter setting, the ROM serves as a means to accelerate the Monte Carlo convergence, relying ultimately on the FEM to establish unbiased predictions.

The second approach will be the use of surrogate models, offering an entirely data-driven mathematical approximation of the input/output relationships of the high-fidelity model. For addressing aleatoric uncertainties in the hazard description (i.e., the so-called ground-motion to ground-motion variability), a stochastic Gaussian Process (GP) emulation approach is adopted to directly approximate the EDP distribution (considering the influence of the aleatoric uncertainties). Improvements in computational efficiency are promoted by avoiding any replications for the stochastic GP implementation. The extension to vector EDP outputs is also briefly discussed, accommodated by approximating the correlation matrix.

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.

UQSay #81

The eighty-first UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, January 23, 2025.

2–3 PM — Congye Wang (Newcastle University, UK) — [slides]

Reinforcement Learning for Adaptive MCMC

An informal observation, made by several authors, is that the adaptive design of a Markov transition kernel has the flavour of a reinforcement learning task. Yet, to date it has remained unclear how to actually exploit modern reinforcement learning technologies for adaptive MCMC. The aim of this talk is to set out a general framework, called Reinforcement Learning Metropolis–Hastings, that we argue can be theoretically supported. Our principal focus is on learning fast-mixing Metropolis–Hastings transition kernels, which we cast as deterministic policies and optimise via a policy gradient. Preliminary results on the PosteriorDB benchmark will be presented.

References:

• Reinforcement Learning for Adaptive MCMC, 2024 - [Github]

Joint work with W. Chen (University of Sydney) & H. Kanagawa (Newcastle University) & C. J. Oates (Newcastle University - Alan Turing Institute).

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.

UQSay #80

The eightieth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, December 12, 2024.

2–3 PM — Claire Boyer (LMO, UPS) — [slides]

A primer on physics-informed learning

Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a partial differential equation that quantifies the physical inconsistency. Practitioners often resort to physics-informed neural networks (PINNs) to solve this kind of problem. After discussing some strengths and limitations of PINNs, we prove that for linear differential priors, the problem can be formulated directly as a kernel regression task, giving a rigorous framework to analyze physics-informed ML. In particular, the physical prior can help in boosting the estimator convergence. We also propose the PIKL algorithm (PIKL for physics-informed kernel learning) as a numerical strategy to implement this kernel method.

References:

• Convergence and error analysis of PINNs, Bernoulli 2024
• Physics-informed machine learning as a kernel method, 2024
• Physics-informed kernel learning, 2024

Joint work with N. Doumèche (Sorbonne University) & G. Biau (Sorbonne University) & F. Bach (INRIA).

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.

UQSay #79

The seventy-ninth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, November 28, 2024.

2–3 PM — Sam Allen (ETH Zürich, Seminar of Statistics) — [slides]

Evaluating forecasts using positive definite kernels

Probabilistic forecasts take the form of probability distributions over the set of possible outcomes. To assess the quality of a probabilistic forecast, proper scoring rules condense forecast performance into a single numerical value, with which competing forecasters can be ranked and compared. Many popular scoring rules can be expressed in terms of positive definite kernels. This allows us to leverage well-established results on kernels when evaluating probabilistic forecasts. In this work, we discuss two useful connections between kernel methods and scoring rules. Firstly, we demonstrate that well-known weighted scoring rules correspond to kernel scores. Weighted scoring rules allow users to emphasise particular outcomes during forecast evaluation, and by expressing these as kernel scores, we introduce a broad generalisation of existing weighted scores that can be applied to probabilistic forecasts on arbitrary outcome domains. This facilitates the introduction of weighted multivariate scoring rules, for example. Secondly, we demonstrate that by embedding probabilistic forecasts into a Reproducing Kernel Hilbert Space (RKHS), estimating the parameters of forecast models by optimising a kernel score often corresponds to a convex quadratic optimisation problem, which can therefore be solved robustly and efficiently. This encompasses common forecast combination methods, such as linear pooling, providing a means to optimally combine competing forecasts made on arbitrary outcome domains. To illustrate the practical benefit of these results, the two applications of kernel scores are applied in case studies on operational weather forecasts..

References:

• Evaluating Forecasts for High-Impact Events Using Transformed Kernel Scores, 2023
• Weighted scoringRules: Emphasizing Particular Outcomes When Evaluating Probabilistic Forecasts, 2024 - [R package]- [Python package]
• Efficient pooling of predictions via kernel embeddings, 2024

Joint work with D. Ginsbourger (University of Bern) & J. Ziegel (ETH Zürich).

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.

UQSay #78

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.