Friday, January 27, 2023

UQSay #54

The fifty-fourth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, February 2, 2022.

2–3 PM — Brian Staber (Safran Tech) — [slides]


Quantitative performance evaluation of Bayesian neural networks

Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Various approaches have been investigated including Bayesian neural networks, ensembles, deterministic approximations, amongst others. Despite the growing litterature about uncertainty quantification in deep learning, the quality of the uncertainty estimates remains an open question. In this work, we attempt to assess the performance of several algorithms on sampling and regression tasks by evaluating the quality of the confidence regions and how well the generated samples are representative of the unknown target distribution. Towards this end, several sampling and regression tasks are considered, and the selected algorithms are compared in terms of coverage probabilities, kernelized Stein discrepancies, and maximum mean discrepancies.

Joint work with Sébastien Da Veiga (ENSAI).

Ref: arXiv:2206.06779

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.

Monday, January 16, 2023

UQSay #53

The fifty-third UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, January 19, 2022.

2–3 PM — Felipe Tobar (Initiative for Data & AI, Univ. de Chile) — [slides]


Computationally-efficient initialisation of Gaussian processes: The generalised variogram method

We present a computationally-efficient strategy to find the hyperparameters of a Gaussian process (GP) avoiding the computation of the likelihood function. Motivated by the fact that training a GP via ML is equivalent (on average) to minimising the KL-divergence between the true and learnt model, we set to explore different metrics/divergences among GPs that are computationally inexpensive and provide estimates close to those of ML. In particular, we identify the GP hyperparameters by projecting the empirical covariance or (Fourier) power spectrum onto a parametric family, thus proposing and studying various measures of discrepancy operating on the temporal or frequency domains. Our contribution extends the Variogram method developed by the geostatistics literature and, accordingly, it is referred to as the Generalised Variogram method (GVM). In this talk, we will start with a brief introduction to Gaussian processes, then present the proposed GVM and finally provide experimental validation using synthetic and real-world data.

Joint work with Elsa Cazelles & Taco de Wolff.

Ref: arXiv:2210.05394.

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.

Monday, January 2, 2023

UQSay #52

The fifty-second UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, January 5, 2023.

2–3 PM — Georgios Karagiannis (Durham University)


Bayesian spanning treed co-kriging for high dimensional output emulation

We propose a new Bayesian emulator, called Bayesian spanning treed co-kriging, suitable to analyze computer models with non-stationary massive outputs in the multifidelity setting. Our motivation comes from a real-life application with a storm surge simulator. Given certain assumptions on the Bayesian model, we introduce a suitable stochastic mechanism that facilitates predictions in a principal manner. The good performance of our method is demonstrated in benchmark examples, while our method is implemented for the analysis of a surge simulator given simulations at different fidelity levels.

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.

Saturday, November 12, 2022

UQSay #51

The fifty-first UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, November 17, 2022.

2–3 PM — Cécile Mercadier (Institut Camille Jordan) — [slides]


Hoeffding–Sobol and Möbius decompositions for (tail-)dependence analysis

Methods to analyse dependence and tail dependence are well established. Using for instance the copula function or the stable tail dependence function, and their empirical versions, one can construct non parametric statistics, parametric inference, as well as testing or resampling procedures. My talk will reflect upon the use of g sensitivity analysis for extreme value theory and copula modeling. Through my recent publications, I will explain what their links are and the benefit in mixing these domains.

Joint work with Christian Genest, Paul Ressel & Olivier Roustant.

Refs:

  • C. Mercadier, O. Roustant & C. Genest (2022). Linking the Hoeffding–Sobol and Möbius formulas through a decomposition of Kuo, Sloan, Wasilkowski, and Wozniakowski. Statistics & Probability Letters, vol. 185 [hal-03220809],
  • C. Mercadier & P. Ressel (2021). Hoeffding–Sobol decomposition of homogeneous co-survival functions: from Choquet representation to extreme value theory application. Dependence Modeling, 9(1):179–198 [hal-03200817],
  • C. Mercadier & O. Roustant (2019). The tail dependograph. Extremes, 22:343–372 [hal-01649596].

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.

Tuesday, October 4, 2022

UQSay #50

The fiftieth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, October 13, 2022.

2–3 PM — Gilles Stoltz (LMO, Université Paris-Saclay - CNRS) — [slides]


Multi-armed bandit problems: a statistical view, focused on lower bounds

Multi-armed bandit problems correspond to facing K unknown probability distributions, having to sequentially pull one of them, and observing a realization thereof at each pull. Two goals will be considered.

(1) The realizations are payoffs, and the sum of these payoffs is to be maximized. This goal is achieving by minimizing regret, which is defined as the expected performance of the best arm minus the expected sum of payoffs achieved by a strategy. Two types of bounds may be defined, depending on whether they may depend on the specific bandit problem or only on the model (the class of possible distributions). We will recall classical strategies like UCB and MOSS, as well as a new strategy combining both, called KL-UCB-Switch. We will review upper bounds on the regret and detail which lower bounds may be achieved, and how. We will deal with one interesting extension, the adaptation to the unknown range of the distributions, i.e., when the distribution are supported on a compact interval that is unknown as well.

The case of regret minimization is very well understood in the literature, contrary to:

(2) A second goal can be to identify the best arm, i.e., control the probability that after T observations (sampled adaptively) the strategy does not identify the arm with the highest expectation. This is called best arm identification with a fixed budget. Limited results are available. We will describe a typical strategy, called successive rejects, that drops one distribution after the other after horse racing them. We will also indicate how we are currently laying the foundations of a non-parametric approach to this problem, based on KL divergences, as opposed to typical approaches based on differences between expectations.

Joint work with Antoine Barrier, Aurélien Garivier, Hédi Hadiji & Pierre Ménard.

Refs:

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.

Wednesday, September 21, 2022

UQSay #49

The forty-ninth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, September 29, 2022.

2–3 PM — Jonas Latz (Heriot-Watt University, Edinburgh) — [slides]


Stochastic gradient descent in continuous time: discrete and continuous data

Optimisation problems with discrete and continuous data appear in statistical estimation, machine learning, functional data science, robust optimal control, and variational inference. The "full" target function in such an optimisation problem is given by the integral over a family of parameterised target functions with respect to a discrete or continuous probability measure. Such problems can often be solved by stochastic optimisation methods: performing optimisation steps with respect to the parameterised target function with randomly switched parameter values. In this talk, we discuss a continuous-time variant of the stochastic gradient descent algorithm. This so-called stochastic gradient process couples a gradient flow minimising a parameterised target function and a continuous-time 'index' process which determines the parameter.

We first briefly introduce the stochastic gradient processes for finite, discrete data which uses pure jump index processes. Then, we move on to continuous data. Here, we allow for very general index processes: reflected diffusions, pure jump processes, as well as other Lévy processes on compact spaces. Thus, we study multiple sampling patterns for the continuous data space. We show that the stochastic gradient process can approximate the gradient flow minimising the full target function at any accuracy. Moreover, we give convexity assumptions under which the stochastic gradient process with constant learning rate is geometrically ergodic. In the same setting, we also obtain ergodicity and convergence to the minimiser of the full target function when the learning rate decreases over time sufficiently slowly.

Joint work with Kexin Jin, Chenguang Liu & Carola-Bibiane Schönlieb.

Refs: DOI:10.1007/s11222-021-10016-8, arXiv:2112.03754, arXiv:2203.11555.

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.

Tuesday, May 24, 2022

UQSay #48

The forty-eighth UQSay seminar on UQ, DACE and related topics will take place online on Thursday afternoon, June 2, 2022.


2–3 PM — Valentin Resseguier (Scalian Innovation Lab, INRAE) — [slides]


Fast generation of prior for Bayesian estimation problems in fluid mechanics

We are interested in real-time estimation and short-term forecasting of 3D fluid flows, using limited computational resources. This is possible through the coupling between data, numerical simulations and sparse fluid flow measurements. Here, the term data refers to numerical simulation outputs. To achieve these ambitious goals, synthetic (i.e. simulated) data and intrusive surrogate models drastically reduce the problem dimensionality – typically from 10 7 to 10. Unfortunately, even with corrections, the accumulated errors of these surrogate models increase rapidly over time due to the chaotic and intermittent nature of fluid mechanics. Therefore, deterministic predictions are hardly possible outside the learning time interval. Data assimilation can alleviate these problems by (i) providing a set of simulations covering probable futures (without increasing the computational cost) and (ii) constraining these online simulations with measurements.

We addressed this Uncertainty Quantification (UQ) problem (i) with a multi-scale physically-based stochastic parameterization called "Location uncertainty models" (LUM) [1-3] and new statistical estimators based on stochastic calculus, signal processing and physics [3]. The deterministic ROM coefficients are obtained by a Galerkin projection whereas the correlations of the noises are estimated from the residual velocity, the physical model structure, and the evolution of the resolved modes. We solved problem (ii) with a particle filter [4].

Whether we consider UQ [3] or DA [4] applications, our method greatly exceeds the state of the art, for ROM degrees of freedom smaller than 10 and moderately turbulent 3D flows (Reynolds number up to 300).

Joint work A. M. Picard & M. Ladvig (Scalian), and D. Heitz (INRAE).

Refs: [1] hal-01391420, [2] hal-02558016, [3] hal-03169957 & [4] hal-03445455.

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).

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.