# Séminaire UQSay

## UQSay: UQ, DACE & sujets connexes @ Paris-Saclay

UQSay est un séminaire régulier sur le thème de la quantification d’incertitude au sens large (En savoir plus…), organisé par le L2S, MSSMAT, le LMT et EDF R&D.

## Tous les séminaires

### UQSay #33

The thirty-third UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, July 1, 2021.

#### Reliability sensitivity analysis with FORM

This talk discusses reliability sensitivity analysis with the first-order reliability method (FORM). Classical sensitivity indices, which are often used to assess the influence of the input random variables on the probability of failure, are the FORM $\alpha$-factors. These factors are the directional cosines of the the most likely failure point in an underlying independent standard normal space and are obtained as by-products of the FORM analysis. The talk reviews a set of alternative reliability sensitivity indices and their estimation with FORM. Focus is put on variance-based reliability sensitivities that emerge from the variance decomposition of the indicator function of the failure event. The resulting first-order and total-effect reliability sensitivities can be estimated as a function of the FORM reliability indices and the $\alpha$-factors. The second part of the talk addresses decision-oriented sensitivities based on the concept of value of information. In particular, the indices associated with a decision related to the safety of an existing system are presented and their estimation with FORM is examined. The accuracy of the FORM approximations of the various sensitivities is demonstrated with numerical examples. Joint work with Daniel Straub. Ref: DOI:10.1016/j.ress.2021.107496 (preprint) and arxiv:2104.00986.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #32

The thirty-second UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, June 17, 2021.

#### Probabilistic Full-Waveform Inversion

In the course of the past decade, full-waveform inversion has matured from a largely idealistic dream into a commonly applied method to image the internal structure of inaccessible bodies. Despite undeniable success, a major problem remains: The quantification of uncertainties in this often strongly nonlinear inverse problem. In this lecture, I will present a series of computational approaches that brings probabilistic full-waveform inversion with complete uncertainty quantification within reach: 1) Hamiltonian Monte Carlo sampling of the posterior probability density treats model parameters as particles that orbit through model space, obeying Hamilton’s equations from classical mechanics. The scaling properties of Hamiltonian Monte Carlo allow us to consider high-dimensional model spaces that often cannot be considered with more traditional, derivative-free sampling methods. 2) Autotuning based on limited-memory quasi-Newton methods provides nearly optimal mass matrices for Hamiltonian Monte Carlo, thereby largely removing laborious manual tuning. A factorised version of the L-BFGS algorithm, in particular, can increase the effective sample size by more than an order of magnitude. 3) Wavefield-adapted spectral-element meshes exploit prior knowledge on the geometry of wavefields. Such prior knowledge is frequently available for media that are smooth relative to the minimum wavelength. Wavefield-adapted meshes have the potential to drastically reduce the number of elements, leading to a computational forward modelling cost that makes Monte Carlo sampling possible. Joint work with Lars Gebraad & Christian Boehm. Ref: DOI:10.1029/2019JB018428.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #31

The thirty-first UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, June 3, 2021.

#### Uncertainty Quantification in graphs of functions through sample reweighting

The needs for multidisciplinary simulations in the design of complex industrial systems motivate the development of Uncertainty Quantification and Sensitivity Analysis methods that are compatible with disciplinary autonomy. This presentation focuses on decomposition methods based on sample reweighting. The design process is modeled by a graph, whose nodes are simulation codes and edges are exchanges of variables. The first part of this presentation is dedicated to the study of one particular reweighting method, based on the minimization of a Wasserstein distance. An explicit expression of the weights is exhibited in terms of Nearest Neighbors and some consistency results and rates of convergence are derived. The second part is dedicated to the general propagation of the weights in directed acyclic graphs, inspired from an existing algorithm of Amaral, Allaire & Willcox (2014). A general framework is developed to characterize the consistency of the global algorithm in terms of local weighting condition at each node. We observe that some weighting schemes can be obtained naturally from nonparametric linear regressions and linear smoothers. An interesting equivalence with some already existing tools in the literature permits to simplify the numerical computations part. The final algorithm does not require that the simulation codes have to be run at the same time or in a specific order. Hence, it allows for disciplinary autonomy. Joint work with Julien Reygner. Ref: hal-02968059.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #30

The thirtieth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, May 20, 2021.

#### An information geometry approach for robustness analysis in uncertainty quantification of computer codes

Robustness analysis is an emerging field in the uncertainty quantification domain. It involves analyzing the response of a computer model—which has inputs whose exact values are unknown—to the perturbation of one or several of its input distributions. Practical robustness analysis methods therefore require a coherent methodology for perturbing distributions; we present here one such rigorous method, based on the Fisher distance on manifolds of probability distributions. Further, we provide a numerical method to calculate perturbed densities in practice which comes from Lagrangian mechanics and involves solving a system of ordinary differential equations. The method introduced for perturbations is then used to compute quantile-related robustness indices. We illustrate these « perturbed-law based » indices on several numerical models. We also apply our methods to an industrial setting: the simulation of a loss of coolant accident in a nuclear reactor, where several dozen of the model’s physical parameters are not known exactly, and where limited knowledge on their distributions is available. Joint work with Jérôme Stenger, Roman Sueur et Bertrand Iooss. Refs: DOI:10.1080/00401706.2021.1905072.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #30

The thirtieth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, May 20, 2021.

#### An information geometry approach for robustness analysis in uncertainty quantification of computer codes

Robustness analysis is an emerging field in the uncertainty quantification domain. It involves analyzing the response of a computer model—which has inputs whose exact values are unknown—to the perturbation of one or several of its input distributions. Practical robustness analysis methods therefore require a coherent methodology for perturbing distributions; we present here one such rigorous method, based on the Fisher distance on manifolds of probability distributions. Further, we provide a numerical method to calculate perturbed densities in practice which comes from Lagrangian mechanics and involves solving a system of ordinary differential equations. The method introduced for perturbations is then used to compute quantile-related robustness indices. We illustrate these « perturbed-law based » indices on several numerical models. We also apply our methods to an industrial setting: the simulation of a loss of coolant accident in a nuclear reactor, where several dozen of the model’s physical parameters are not known exactly, and where limited knowledge on their distributions is available. Joint work with Jérôme Stenger, Roman Sueur et Bertrand Iooss. Refs: DOI:10.1080/00401706.2021.1905072.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #29

The twenty-ninth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, May 6, 2021.

#### Online damage detection and model updating via proper orthogonal decomposition and recursive Bayesian filters

An approach based on the synergistic use of proper orthogonal decomposition (POD) and Kalman filtering is proposed for the online health monitoring of damaged structures. The reduced-order model of the structure is obtained during the initial training stage of monitoring; afterward, effective estimations of structural damage are provided online by tracking the evolution in time of stiffness parameters and projection bases handled in the model order reduction procedure. Such tracking is accomplished via two Kalman filters: a first one to deal with the time evolution of a joint state vector, gathering the reduced-order state and the stiffness terms degraded by damage; a second one to deal with the update of the reduced-order model in case of damage evolution. Both filters exploit the information conveyed by measurements of the structural response to the external excitations. Focusing on multi-story shear building, the capability and performance of the proposed approach are assessed in terms of tracked variation of the stiffness terms, identified damage location and speed-up of the whole health monitoring procedure. Joint work with Saeed Eftekhar Azam, Giovanni Capellari, Francesco Caimmi. Refs: 10.1016/j.engstruct.2017.12.031, 10.1007/s11071-017-3530-1, 10.3390/s16010002, 10.1504/IJSMSS.2015.078355, 10.1016/j.engstruct.2013.04.004.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #28

The twenty-eighth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, April 22, 2021.

#### Optimal Thinning of MCMC Output

There is a recent trend in computational statistics to move away from sampling methods and towards optimisation methods for posterior approximation. These include discrepancy minimisation, gradient flows and control functionals—all of which have the potential to deliver faster convergence than a Monte Carlo method. In this talk we will see how ideas from discrepancy minimisation can be applied to the problem of optimal thinning of MCMC output. Joint work with Marina Riabiz, Wilson Chen, Jon Cockayne, Pawel Swietach, Steve Niederer, Lester Mackey. Ref: arXiv:2005.03952 and http://stein-thinning.org.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #27

The twenty-seventh UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, April 1, 2021.

#### Bayesian optimization of variable-size design space problems

Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables. Additionally, complex system design problems occasionally present a variable-size design space. This results in an optimization problem for which the search space varies dynamically (with respect to both number and type of variables) along the optimization process as a function of the values of specific discrete decision variables. Similarly, the number and type of constraints can vary as well. In this paper, two alternative Bayesian optimization-based approaches are proposed in order to solve this type of optimization problems. The first one consists of a budget allocation strategy allowing to focus the computational budget on the most promising design sub-spaces. The second approach, instead, is based on the definition of a kernel function allowing to compute the covariance between samples characterized by partially different sets of variables. The results obtained on analytical and engineering related test-cases show a faster and more consistent convergence of both proposed methods with respect to the standard approaches. Joint work with Loic Brevault (ONERA), Mathieu Balesdent (ONERA), El-Ghazali Talbi (Inria Lille), Yannick Guerin (CNES). Ref: arXiv:2003.03300.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #26

The twenty-sixth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, March 18, 2021.

#### Incremental space-filling design based on coverings and spacings: improving upon low discrepancy sequences

The paper addresses the problem of defining families of ordered sequences {x_i} i∈N of elements of a compact subset X of R^d whose prefixes X_n = {x_i} i=1, …, n, for all orders n, have good space-filling properties as measured by the dispersion (covering radius) criterion. Our ultimate aim is the definition of incremental algorithms that generate sequences X_n with small optimality gap, i.e., with a small increase in the maximum distance between points of X and the elements of X_n with respect to the optimal solution X_n. The paper is a first step in this direction, presenting incremental design algorithms with proven optimality bound with respect to one-parameter families of criteria based on coverings and spacings that both converge to dispersion for large values of their parameter. Joint work with Luc Pronzato and Maria-Joao Rendas. Ref: hal-02987983.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #25

The twenty-fifth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, March 4, 2021.

#### Bayesian optimisation: ablation study, global performance assessment and improvements based on trust regions

Bayesian Optimisation algorithms (BO) are global optimisation methods that iterate by constructing and using conditional Gaussian processes (GP). It is a common claim that BO is state-of-the-art for costly functions. However, this claim is weakly supported by experimental evidence, as BO is most often compared to itself, rather than to algorithms of different nature. In this work, we study the performance of BO within the well-known COmparing Continuous Optimizers benchmark (COCO). We first analyse the sensitivity of BO to its own parameters, enabling us to answer general questions regarding the choice of the GP kernel or its trend, the initial GP budget, and the suboptimisation of the acquisition function. Then, we study on which function class and dimension BO is relevant when compared to state-of-the-art optimisers for expensive functions. The second part of this talk describes a new BO algorithm to improve scalability with dimension, called TREGO (trust-region-like efficient global optimisation). TREGO alternates between regular BO steps and local steps within a trust region. By following a classical scheme for the trust region (based on a sufficient decrease condition), we demonstrate that our algorithm enjoys strong global convergence properties, while departing from EGO only for a subset of optimization steps. The COCO benchmark experiments reveal that TREGO consistently outperforms EGO and closes the performance gap with other state-of-the-art algorithms in conditions (high budget and dimension) for which BO was struggling to compete previously. Joint work Youssef Diouane, Rodolphe Le Riche, Alexandre Scotto Di Perrotolo. Ref: arXiv:2101.06808 & DiceOptim.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #24

The twenty-fourth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, February 18, 2021.

#### ICSCREAM methodology for the Identification of penalizing Configurations using SCREening And Metamodel — Application to high-dimensional thermal-hydraulic numerical experiments

In the framework of risk assessment in nuclear accident analysis, best-estimate computer codes are used to estimate safety margins. Several inputs of the code can be uncertain, due to a lack of knowledge but also to the particular choice of accidental scenario being considered. The objective of this work is to identify the most penalizing (or critical) configurations of several input parameters (called “scenario inputs”), independently of the uncertainty of the other inputs. Critical configurations of the scenario inputs correspond to high values of the code output Y, defined here by exceeding the 90%-quantile. However, thermal-hydraulic codes are too CPU-time expensive to be directly used to propagate the input uncertainties and solve the inversion problem. The adopted solution consists in fitting the code output by a metamodel, built from a reduced number of code simulations. When the number of input parameters is very large (e.g., around a hundred here), the metamodel building remains a challenge. To overcome this, we have developed a methodology, called ICSCREAM for Identification of penalizing Configurations using SCREening And Metamodel. Applied from a Monte Carlo sample of code simulations, the ICSCREAM methodology judiciously combines a step of SA to identify and rank the main influential inputs and to reduce the dimension, before building a Gaussian process (GP) metamodel. SA relies on new statistical independence tests that aggregate information of global and target Hilbert-Schmidt independence criteria. The GP is then efficiently built with a sequential process, where the inputs are taken into account in a more or less fine way, according to their supposed influence. Finally, the GP metamodel is intensively used to estimate the conditional probabilities of Y exceeding the critical value, according to each inputs to be penalized. Accurate uncertainty propagation, not feasible with the computational costly model, become therefore accessible with the ICSCREAM methodology. Joint work with Bertrand Iooss (EDF R&D & IMT) and Vincent Chabridon (EDF R&D). Ref: hal-02535146.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #23

The twenty-third UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, February 4, 2021.

#### Global sensitivity analysis for models described by stochastic differential equations

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest. One of the statistical tools used to quantify the influence of each input variable on the quantity of interest are the Sobol’ sensitivity indices. In this paper, we consider stochastic models described by stochastic differential equations (SDE). We focus the study on mean quantities, defined as the expectation with respect to the Wiener measure of a quantity of interest related to the solution of the SDE itself. Our approach is based on a Feynman-Kac representation of the quantity of interest, from which we get a parametrized partial differential equation (PDE) representation of our initial problem. We then handle the uncertainty on the parametrized PDE using polynomial chaos expansion and a stochastic Galerkin projection. Joint work with Pierre Étoré, Dang Khoi Pham & Long Li. Ref: hal-01926919.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #22

The twenty-second UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, January 21, 2021.

#### Implicit Update for Large-Scale Inversion under GP prior

We present an almost matrix-free update method for posterior Gaussian process distributions under sequential observations of linear functionals. By introducing a novel implicit representation of the posterior covariance matrix, we are able to extract posterior covariance information on large grids and to provide a framework for sequential data assimilation when covariance matrices cannot fit in memory. This is useful in Bayesian linear inverse problems with Gaussian priors, where the matrices involved grow quadratically in the number of elements in the discretization grid, creating memory bottlenecks when inverting on fine-grained discretizations. We illustrate our method by applying it to an excursion set recovery task arising from a gravimetric inverse problem on Stromboli volcano. In this setting, we demonstrate computation and sequential updating of exact posterior mean and covariance at resolutions finer than what state-of-the-art techniques can handle and showcase how the proposed framework enables implementing large-scale probabilistic excursion set estimation and also deriving efficient experimental design strategies tailored to this goal. Joint work with David Ginsbourger (Univ. Bern) and Niklas Linde (Univ. Lausanne). Ref: Volcapy (github).
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #20

The twentieth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, December 17, 2020.

#### Inverse methods for damage estimation in concrete given small data sets

One of the main issues in material science is estimation of the constitutive laws given experimental data that may come in different forms ranging from the microscopic images to the macroscopic data collected by strain gauges for example. As data are often heterogeneous, of multi-scale/temporal nature, possibly ambiguous and of low quality due to missing values, the process of learning is often requiring the careful application of existing or design of new data fusion algorithms that are bounded to small data sets. In this talk will be presented the computationally efficient Bayesian algorithms for the damage estimation. In particular, the special attention will be paid to damage model estimation by using both classical uncertainty quantification as well as machine/deep learning approaches. Joint work with (alphabetical order) X. Chapeleau, P.-E. Charbonnel, L.-M. Cottineau, L. De Lorenzis, A. Ibrahimbegovic, V. Le Corvec, H.G. Matthies, E. Merliot, M.S. Sarfaraz, D. Siegert, R. Vidal, J. Waeytens and T. Wu. Refs: hal-01379214, arXiv:1909.07209, DOI:10.1007/s00466-020-01942-x, arXiv:1912.03108.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #19

The nineteenth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, December 3, 2020.

#### Functional outlier detection applied to nuclear transient simulation analysis

The ever increasing recording and storing capabilities of industrial systems provide a large amount of physical data that can be exploited by engineers. These data may take the form of functions, usually a one-dimensional function of time, but eventually as a multidimensional function of space and time. Finding the subsets of objects that behave abnormally in them is a goal that can prove to be useful in order to avoid spurious results, simulations that do not reproduce certain physical phenomena as expected, or extreme physical events and domains. In the context of nuclear transient simulations, safety reports mostly focus on the study of some scalar parameters (safety criteria), supposed to guarantee the safety of an installation during an accidental transient as long as they do not surpass a previously established threshold. Nevertheless, the state- of-the-art simulations codes (called Best Estimate) provide a much richer and complex information, which can be better taken advantage of through the identification outlying simulations amongst those generated as outputs.   The goal of this talk is to introduce the functional outlier detection domain, highlighting its interest in industrial settings, as well as to present our detection technique and the conclusions on the physical analysis of nuclear transients that can be obtained from its use. Joint work with Mathieu Couplet, Bertrand Iooss, Nathalie Marie, Amandine Marrel, Elsa Merle and Roman Sueur. Reference: hal-02965504.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #18

The eighteenth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, November 19, 2020.

#### Aleatoric and Epistemic Uncertainty in Machine Learning: An Ensemble-based Approach

Due to the steadily increasing relevance of machine learning for practical applications, many of which are coming with safety requirements, the notion of uncertainty has received increasing attention in machine learning research in the last couple of years. This talk will address the question of how to distinguish between two important types of uncertainty, often refereed to as aleatoric and epistemic, in the setting of supervised learning, and how to quantify these uncertainties in terms of suitable numerical measures. Roughly speaking, while aleatoric uncertainty is due to inherent randomness, epistemic uncertainty is caused by a lack of knowledge. As a concrete approach for uncertainty quantification in machine learning, the use of ensemble learning methods will be discussed. Joint work with S. Destercke, V.-L. Nguyen, M. H. Shaker & W. Waegeman. References: arXiv:1910.09457, arXiv:1909.00218, arXiv:2001.00893.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #17

The seventeenth UQSay seminar on UQ, DACE and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, November 5, 2020.

#### 14h–15h — Luc Bonnet (ONERA & MSSMAT) — [slides]

The expected performance of a system can generally differ from its operational performance due to the variability of some parameters. Optimal Uncertainty Quantification is a powerful mathematical tool that can be used to rigorously bound the probability of exceeding a given performance threshold for uncertain operational conditions or system characteristics. Metamodeling is at the heart of this research framework. In this perspective, Kernel Flow, a recent method to obtain a metamodel by kriging developed by Owhadi & Yoo, will be presented. The results obtained will be illustrated by examples in numerical and experimental aerodynamics. Joint work with Eric Savin and Houman Owhadi. References: 10.1016/j.jcp.2019.03.040, 10.1137/10080782X & 10.3390/a13080196.
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #16

The sixteenth UQSay seminar on Uncertainty Quantification and related topics, organized by L2S, MSSMAT, LMT and EDF R&D, will take place online on Thursday afternoon, October 22, 2020.

#### Well-posed stochastic inversion in uncertainty quantification, with links with sensitivity analysis

Stochastic inversion problems are typically encountered when it is wanted to quantify the uncertainty affecting the inputs of computer models. They consist in estimating input distributions from noisy, observable outputs, and such problems are increasingly examined in Bayesian contexts where the targeted inputs are affected by a mixture of aleatory and epistemic uncertainties. While they are characterized by identifiability conditions, well-posedness constraints of « signal to noise » have to be took into account within the definition of the model, prior to inference. In addition to numeric conditioning notions and regularization techniques used in inverse problems, we propose and investigate an interpretation of well-posedness, in the context of parametric uncertainty quantification and global sensitivity analysis, based on the degradation of Fisher information. It offers an explicitation of such prior constraints considering linear or linearizable operators, this linearization being either local (based on differentiability) or variational. Simulated experiments indicate that, when injected into the modeling process, these constraints can limit the influence of measurement or process noise on the estimation of the input distribution, and let hope for future extensions in a full non-linear framework, for example through the use of linear Gaussian mixtures.​
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Amélie Fau (LMT), Bertrand Iooss (EDF R&D).
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 you 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 #15

The fifteenth UQSay seminar on Uncertainty Quantification and related topics, organized by L2S, MSSMAT, and EDF R&D, will take place online on Thursday afternoon, October 8, 2020.

#### Uncertainty Quantification for Maxwell’s eigenproblem based on isogeometric analysis and mode tracking

Superconducting cavities are used in particle accelerators, e.g. at DESY in Hamburg, Germany. Their resonating electromagnetic field is commonly characterised by eigenmodes and eigenvalues which are very sensitive to small geometry deformations. This presentation proposes an uncertainty quantification workflow based on a Karhunen–Loève expansion of the manufacturing imperfections and eigenvalue tracking based on algebraic and geometric homotopies. Joint work with Niklas Georg, Wolfgang Ackermanna, Jacopo Corno. Reference: DOI:10.1016/j.cma.2019.03.002 (arxiv:1802.02978).
Organizing committee: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Bertrand Iooss (EDF R&D).
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 you 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 #14

The fourteenth UQSay seminar on Uncertainty Quantification and related topics, organized by L2S, MSSMAT, and EDF R&D, will take place online on Thursday afternoon, September 24, 2020.

14h–15h — Amélie Fau (LMT, ENS Paris-Saclay)

Alternative strategies for adaptive sampling for kriging metamodels

A large variety of strategies have been proposed in the literature to offer optimal dataset for kriging metamodels. Even though adaptive schemes guarantee convergence and improvement of estimation accuracy for instance for Galerkin approaches at least in a goal-oriented sense, using usual adaptive sampling schemes for kriging metamodels might be detrimental, worsing prediction results compared to one-shot sampling techniques. The goal of this seminar is to share our experience on cases leading to this disvantageous behavior. Besides, problems leading to beneficial behavior will be discussed to highlight criteria for deciding about cases of interest for which adaptive sampling strategies are highly promising.

Joint work with Jan Fuhg & Udo Nackenhorst (Leibniz Universität, Hannover).

Reference: DOI:10.1007/s11831-020-09474-6.

Organizers: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Bertrand Iooss (EDF R&D).

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 you 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 #13

The thirteenth UQSay seminar on Uncertainty Quantification and related topics, organized by L2S, MSSMAT, and EDF R&D, will take place online on Thursday afternoon, September 10, 2020.

14h–15h — Balázs Kégl (Noah’s Ark Lab, Huawei Paris) — [slides]

DARMDN: Deep autoregressive mixture density nets for dynamical system modelling

Unlike computers, physical engineering systems (such as data center cooling or wireless network control) do not get faster with time. This is arguably one of the main reasons why recent beautiful advances in deep reinforcement learning (RL) stay mostly in the realm of simulated worlds and do not immediately translate to practical success in the real world. In order to make the best use of the small data sets these systems generate, we develop data-driven neural simulators to model the system and apply model-based control to optimize them. In this talk I will present the first step of this research agenda, a new versatile system modelling tool called deep autoregressive mixture density net (DARMDN – pronounced darm-dee-en). We argue that the performance of model-based reinforcement learning is partly limited by the approximation capacity of the currently used conditional density models and show how DARMDN alleviates these limitations. The model, combined with a random shooting controller, establishes a new state of the art on the popular Acrobot benchmark. Our most interesting and counter-intuitive finding is that the “sincos” Acrobot system which requires no multimodal posterior predictives, can be solved with a deterministic model, but only if it is trained as a probabilistic model. A deterministic model that is trained to minimize MSE leads to prediction error accumulation.

Joint work with Gabriel Hurtado and Albert Thomas.

Organizers: Julien Bect (L2S), Emmanuel Vazquez (L2S), Didier Clouteau (MSSMAT), Filippo Gatti (MSSMAT), Fernando Lopez Caballero (MSSMAT), Bertrand Iooss (EDF R&D).

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 you 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 #07

The seventh UQSay seminar on Uncertainty Quantification and related topics, organized by L2S and MSSMAT, will take place on Thursday afternoon, January 16, 2020, at CentraleSupelec Paris-Saclay (Eiffel building, amphi III).

We will have two talks: 14h — Bertrand Iooss (EDF R&D / PRISME dept.) — [slides]

Iterative estimation in uncertainty and sensitivity analysis

While building and using numerical simulation models, uncertainty and sensitivity analysis are invaluable tools. In engineering studies, numerical model users and modellers have shown high interest in these techniques that require to run many times the simulation model with different values of the model inputs in order to compute statistical quantities of interest (QoI, i.e. mean, variance, quantiles, sensitivity indices…). In this talk we will focus on new issues relative to large scale numerical systems that simulate complex spatial and temporal evolutions. Indeed, the current practice consists in the storage of all the simulation results. Such a storage becoming quickly overwhelming, with the associated long read time that makes cpu time consuming the estimation of the QoI. One solution consists in avoiding this storage and in computing QoI on the fly (also called in-situ). It turns the problem to considering problems of iterative statistical estimation. The general mathematical and computational issues will be posed, and a particular attention will be paid to the estimation of quantiles (via an adaptation of the Robbins-Monro algorithm) and variance-based sensitivity indices (the so-called Sobol’ indices).

Joint work with Yvan Fournier (EDF), Bruno Raffin (INRIA), Alejandro Ribés (EDF), Théophile Terraz (INRIA).

### UQSay #03

The third UQSay seminar, organized by L2S and EDF R&D, will take place on Thursday afternoon, June 13, 2019, at CentraleSupelec Paris-Saclay (Eiffel building, amphi V). We will have two talks:
14h — Alexandre Janon (Laboratoire de Mathématique d’Orsay) — [slides]

Part 1: Consistency of Sobol indices with respect to stochastic ordering of input parameters

In the past decade, Sobol’s variance decomposition have been used as a tool – among others – in risk management. We show some links between global sensitivity analysis and stochastic ordering theories. This gives an argument in favor of using Sobol’s indices in uncertainty quantification, as one indicator among others. Reference: https://doi.org/10.1051/ps/2018001 (hal-01026373)

Part 2: Global optimization using Sobol indices

We propose and assess a new global (derivative-free) optimization algorithm, inspired by the LIPO algorithm, which uses variance-based sensitivity analysis (Sobol indices) to reduce the number of calls to the objective function. This method should be efficient to optimize costly functions satisfying the sparsity-of-effects principle. Reference: hal-02154121
15h — Pierre Barbillon (MIA Paris) — [slides]

Sensitivity analysis of spatio-temporal models describing nitrogen transfers, transformations and losses at the landscape scale

Modelling complex systems such as agroecosystems often requires the quantification of a large number of input factors. Sensitivity analyses are useful to determine the appropriate spatial and temporal resolution of models and to reduce the number of factors to be measured or estimated accurately. Comprehensive spatial and temporal sensitivity analyses were applied to the NitroScape model, a deterministic spatially distributed model describing nitrogen transfers and transformations in rural landscapes. Simulations were led on a theoretical landscape that represented five years of intensive farm management and covering an area of 3km2. Cluster analyses were applied to summarize the results of the sensitivity analysis on the ensemble of model outputs.The methodology we applied is useful to synthesize sensitivity analyses of models with multiple space-time input and output variables and could be ported to other models than NitroScape. Reference: https://doi.org/10.1016/j.envsoft.2018.09.010 (arXiv:1709.08608)
Organizers: Julien Bect (L2S) and Bertrand Iooss (EDF R&D). No registration is needed, but an email would be appreciated if you intend to come.

### UQSay #01

The first UQSay seminar, organized by L2S, will take place in the afternoon of March 21, 2019, at CentraleSupelec Paris-Saclay (Eiffel building, amphi IV).  We will have two talks:

14h – Mickaël Binois (INRIA Sophia-Antipolis)  [slides]

Heteroskedastic Gaussian processes for simulation experiments

An increasing number of time-consuming simulators exhibit a complex noise structure that depends on the inputs. To conduct studies with limited budgets of evaluations, new surrogate methods are required to model simultaneously the mean and variance fields. To this end, we present recent advances in Gaussian process modeling with input-dependent noise. First, we describe a simple, yet efficient, joint modeling framework that rely on replication for both speed and accuracy. Then we tackle the issue of leveraging replication and exploration in a sequential manner for various goals, such as obtaining a globally accurate model, for optimization, contour finding, and active subspace estimation. We illustrate these on applications coming from epidemiology and inventory management.

Ref : https://arxiv.org/abs/1710.03206.

15h – François Bachoc (IMT, Toulouse)  [slides]

Gaussian process regression model for distribution inputs

Monge-Kantorovich distances, otherwise known as Wasserstein distances, have received a growing attention in statistics and machine learning as a powerful discrepancy measure for probability distributions. In this paper, we focus on forecasting a Gaussian process indexed by probability distributions. For this, we provide a family of positive definite kernels built using transportation based distances. We provide asymptotic results for covariance function estimation and prediction. We also provide numerical comparisons with other forecast methods based on distribution inputs.

Ref : https://arxiv.org/abs/1701.09055.

Organizers : Julien Bect (L2S) and Emmanuel Vazquez (L2S).

No registration is needed, but an email would be appreciated if you intend to come.