Program

 

Preliminary program
 
The conference will start on Wednesday, March 21, at 9:30, and end on Friday, March 23, at 16:30.
 
Download the program here

Wednesday, March 21

9h00-9h30 Welcome of participants   
9h30-9h45 Welcome Speech   
9h45-10h45 Guillaume Obozinski A unified perspective on convex structured sparsity for vectors 
(abstract) SlidesI will present an attempt at a unified theory for convex structured sparsity-inducing norms on vectors associated with combinatorial penalty functions. Specifically, we consider the situation of a model simultaneously (a) penalized by a set-function defined on the support of the unknown parameter vector which represents prior knowledge on supports, and (b) regularized in p-norm. We show that each of the obtained combinatorial optimization problems admits a natural relaxation as an optimization problem regularized by a matching sparsity-inducing norm. To characterize the tightness of the relaxation, we introduce a notion of lower combinatorial envelope of a set-function. Symmetrically, a notion of upper combinatorial envelope produces the most concise norm expression. We show that these relaxations take the form of combinatorial latent group Lassos associated with min-cover penalties also known as block-coding schemes. For submodular penalty functions, the associated norm, dual norm and the corresponding proximal operator can be computed efficiently using a generic divide-and-conquer algorithm. Our framework obtains constructive derivations for the Lasso, group Lasso, exclusive Lasso, the OWL, OSCAR and SLOPE penalties, the k-support norm, several hierarchical penalties considered in the literature for chains and tree structures, and produces also new norms. It leads to general efficient algorithms for all these norms, recovering as special cases several algorithms proposed in the literature and yielding improved procedures for some cases. For norms associated with submodular penalties, including a large number of non-decomposable norms, we generalize classical support recovery and fast rates convergence results based respectively on generalization of the irrepresentability condition and the restricted eigenvalue condition. (Joint work with Francis Bach)
10h45-11h00 Coffee break   
11h00-11h30 Joseph Mure  Gibbs Reference Posterior for Robust Gaussian Process Emulation (abstract)
11h30-12h00 Sophie Marque-Pucheu Surrogate modeling of two nested codes with a functional intermediary variable (abstract)
12h00-12h30 Mélina Ribaud Robustness criterion for kriging based optimization (abstract)
12h30-14h00 Lunch  
14h00-14h30 Malek Ben Salem  Split, doubt and design in high dimension with general surrogates (abstract)
14h30-15h00 Erwan Grelier Statistical learning in tree-based tensor format (abstract) Slides
15h00-15h30 Poster Blitz 1  
 

Lucie Bernard

 Estimating a Probability of Failure with Adaptive Multilevel Splitting (abstract) Poster
  Soumaya Azzi

Stochastic metamodeling applied to dosimetry (abstract) Poster
  Baptiste Broto Efficient estimation of the Shapley sensitivity indices for the linear Gaussian model with independent groups of variables (abstract)
  Mathieu Carmassi Bayesian calibration for computational codes (abstract)
  Vincent Chabridon Reliability-based sensitivity analysis under distribution parameter uncertainty – Application to aerospace systems (abstract) Poster
  Anouar Meynaoui Statistical methodology for second level sensitivity analysis for numerical simulators (abstract)
  Mohamed Reda El Amri Stochastic Inversion Under Functional Uncertainties (abstract)
  Kévin Elie-dit-Cosaque Shapley effects for sensitivity analysis with dependent inputs (abstract)
  Edouard Fournier Influence of Dimension Reduction on regression trees-based Algorithms - Predicting Aeronautics Loads of a Derivative Aircraft (abstract)
 

David Gaudrie

Targeting Well-Balanced Solutions in Bayesian Multi-Objective Optimization under a Restricted Budget (abstract)
  Grégory Delipei

Shapley indices estimation in multi-physics nuclear transient modeling (abstract) Poster
15h30-16h00 Coffee break   
16h00-16h30 Nazih Benoumechiara Quantile Estimation in Structural Reliability with Incomplete Dependence Structure (abstract) Slides
16h30-17h00 Antoine Usseglio-Carleve Quantile prediction of a random field extending the gaussian setting (abstract) Slides
17h00-17h30 Poster blitz 2  
   Alexandre Goupy Polynomial chaos expansion for acoustic propagation (abstract)
   David Lebel Bayesian calibration using Gaussian surrogate model of the likelihood function: application to train suspensions monitoring (abstract) Poster
 

 Andres Felipe Lồpez-Lopera

 Gaussian process regression models under linear inequality conditions (abstract)
   Mickael Rivier Low-cost optimization under uncertainty through box representation of robustness measures (abstract) Poster
   François Sanson Uncertainty quantification in large systems of solvers: application to reentering man-made space object trajectory prediction (abstract)
   Aldo Serafino Assessment of Uncertainty Quantification Methods with Application to the Design of Organic Rankine Cycles (abstract) Poster
   Adrien Spagnol

Global sensitivity analysis for optimization with variable selection (abstract)
   Uladzislau Stazhynski Uncertainty Quantification for Stochastic Approximation Limits Using Chaos Expansion (abstract) Poster
   Léonard Torossian A review on quantile regression for stochastic computer experiments (abstract)
   Xujia Zhu

Surrogating the response PDF of stochastic simulators using semi-parametric representations (abstract)
  Thomas Galtier

The interacting particle system estimation method with piecewise deterministic Markovian processes (abstract) Poster
17h30-18h30 Poster session   
18h30-19h30 Cocktail   

 

Thursday, March 22

9h00-10h30 Julien Mairal Course: Foundations of Deep Learning from a Kernel Point of View 
(abstract) SlidesIn the past years, deep neural networks such as convolutional or recurrent ones have become highly popular for solving various prediction problems, notably in computer vision and natural language processing. Conceptually close to approaches that were developed several decades ago, they greatly benefit from the large amounts of labeled data that have been available recently, allowing to learn huge numbers of model parameters without worrying too much about overfitting. Before the resurgence of neural networks, non-parametric models based on positive definite kernels were one of the most dominant topics in machine learning. These approaches are still widely used today because of several attractive features. Kernel methods are indeed versatile; as long as a positive definite kernel is specified for the type of data considered—e.g., vectors, sequences, graphs, or sets—a large class of machine learning algorithms originally defined for linear models may be used. Kernel methods also admit natural mechanisms to control the learning capacity and reduce overfitting. In this lecture, we will consider both paradigms and show how they are related. We will notably show that the reproducing kernel point of view allows to derive theoretical results for classical convolutional neural networks.
10h30-11h00 Coffee break   
11h00-11h45 Gabriel Peyré Computational Optimal Transport for Imaging and Learning 
(abstract) SlidesOptimal transport (OT) has become a fundamental mathematical tool at the interface between calculus of variations, partial differential equations and probability. It took however much more time for this notion to become mainstream in numerical applications. This situation is in large part due to the high computational cost of the underlying optimization problems. There is a recent wave of activity on the use of OT-related methods in fields as diverse as computer vision, computer graphics, statistical inference, machine learning and image processing. In this talk, I will review an emerging class of numerical approaches for the approximate resolution of OT-based optimization problems. This offers a new perspective for the application of OT in imaging sciences (to perform color transfer or shape and texture morphing) and machine learning (to perform clustering, classification and generative models in deep learning). More information and references can be found on the website of our book "Computational Optimal Transport" https://optimaltransport.github.io/
11h45-12h30 Nelly Pustelnik  Combining multiresolution analysis and non-smooth optimization for texture segmentation 
(abstract) SlidesTexture segmentation represents a major challenge in image processing, especially when dealing with stochastic textures. In this talk, we will address this issue by coupling multiresolution analysis and non-smooth optimization tools. First, we will present the usual two-step estimation/segmentation approach, then we will provide new formulations aiming at performing the two steps together. In a second part, we will focus on refining algorithmic segmentation procedures to obtain low computational methods in order to evaluate the performance of the tools developed on large data volumes such as those encountered in the study of the dynamics of multiphase flows in porous media.
12h30-14h00 Lunch   
14h00-14h45      Claire Boyer On the gap between local recovery guarantees in structured compressed sensing and oracle estimates 
(abstract) SlidesThis is an on-going work with Ben Adcock and Simone Brugiapaglia (Simon Fraser University, Burnaby). First we will introduce a compressed sensing (CS) theory more compatible with real-life applications: we derive guarantees to ensure reconstruction of a structured sparse signal of interest while imposing structure in the acquisition (no Gaussian measurements here...). We will study how far those CS results are from oracle-type guarantees, and we will show that they are similar in terms of the required number of measurements. These results give an insight to design new optimal sampling strategies when realistic physical constraints are imposed in the acquisition.
14h45-15h30 Karim Lounici Principal Component Analysis: a Berry-Esseen Bound for the Spectral Projectors of the Covariance Operator (abstract)
15h30-16h15 Julie Josse Distributed Multi-Level Matrix Completion for Medical Databases 
(abstract) Gathering the information contained in the databases of several hospitals is a step toward personalized medical care as it increases the chances of finding similar patient profiles and therefore provinding them better treatment. However, there are technical (computations and storage issues) and social barriers (privacy concerns) to the aggregation of medical data. Both obstacles can be overcome by turning to distributed computations so that hospitals only share some intermediate results instead of the raw data. As it is often the case, the medical databases are incomplete. One aim of the project is to impute the data of one hospital using the data of the other hospitals. This could also be an incentive to encourage the hospitals to participate in the project. In this talk, we will describe a single imputation method for multi-level (hierarchical) data that can be used to impute both quantitative, categorical and mixed data. This method is based on multi-level simultaneous component analysis (MLSCA) which basically decomposes the variability in both a between and within (hospitals) variability and performs a SVD on each part. The imputation method can be seen as an extension of matrix completion methods. The methods and their distributed versions are implemented in an R package.
16h15-16h45 Coffee break   
16h45-17h30 Anne Ruiz-Gazen Using Invariant Coordinate Selection for outlier detection in high dimension
(abstract) The Invariant Coordinate Selection (ICS) is an affine invariant method which may prove useful in the context of multivariate outlier detection. The method is based on the joint diagonalization of two scatter matrix estimators. It leads to a coordinate system for which the Euclidian distance between observations corresponds to a Mahalanobis distance in the sense of one of the two scatter matrices. The Mahalanobis distance is a well-known tool for detecting multivariate outliers. However, in large dimension (but still more observations than variables), the performance of the Mahalanobis distance is low. By allowing the selection of appropriate components, ICS performs better as soon as the outliers lie in a small dimension subspace. This point will be illustrated on some simulated and real data sets from the industry. Moreover, we will discuss the adaptation of ICS to the case of singular scatter matrix estimators which may happen in case of multicolinearity or high dimensional data.
17h30-18h15 Guillaume Perrin Kernel representations for the approximation of the distribution of high-dimensional random vectors 
(abstract) SlidesThe Gaussian kernel-density estimation (G-KDE) is a powerful tool to identify the distribution of random vectors when the maximal information is a set of independent realizations. For these methods, a key issue is the choice of the kernel and the optimization of the bandwidth matrix. To optimize these kernel representations, two adaptations of the classical G-KDE are presented in this presentation. First, it is suggested to add constraints on the mean and the covariance matrix in the G-KDE formalism. Then, it is proposed to separate in different groups the components of the random vector of interest that could reasonably be considered as independent. Finally, three applications of this tool are shown. The first one concerns the distribution identification of very-high dimensional random vectors. The second one deals with reliability-oriented sensitivity analyses. The last one focuses on the identification of the mechanical properties of a heterogeneous microstructure modeled by a random elastic media.
20h00 Conference dinner  Bar restaurant du Lieu Unique, 2 rue de la bisuiterie, Quai Ferdinand Favre, Nantes

 

Friday, March 23

9h00-10h30 Julien Mairal Course: Optimization methods for large-scale machine learning and sparse estimation 
(abstract) SlidesIn this lecture, we will introduce a few techniques recently introduced in machine learning and optimization to deal with large amounts of data. We will focus on regularized empirical risk minimization problems, which consists of minimizing a large sum of functions, and cover also stochastic optimization techniques for minimizing expectations. Concepts we are planning to cover include stochastic gradient descent techniques with variance reduction, Nesterov's acceleration, and Quasi-Newton techniques. We will also consider variants that allow dealing with nonsmooth regularization such as the l1-norm, which is useful for sparse estimation in high dimension
10h30-11h00 Coffee break   
11h00-11h45 Gérard Biau Optimization by Gradient Boosting (joint work with B. Cadre) 
(abstract) SlidesGradient boosting is a state-of-the-art prediction technique that sequentially produces a model in the form of linear combinations of simple predictors---typically decision trees---by solving an infinite-dimensional convex optimization problem. We provide a thorough analysis of two widespread versions of gradient boosting, and introduce a general framework for studying these algorithms from the point of view of functional optimization. We prove their convergence as the number of iterations tends to infinity and highlight the importance of having a strongly convex risk functional to minimize. We also present a reasonable statistical context ensuring consistency properties of the boosting predictors as the sample size grows. In our approach, the optimization procedures are run forever (that is, without resorting to an early stopping strategy), and statistical regularization is basically achieved via an appropriate L^2 penalization of the loss and strong convexity arguments.
11h45-12h30 Victor Picheny Combining game theory and Bayesian optimization to solve many-objective problems 
(abstract) SlidesOptimization problems with many objectives (more than three) are notoriously difficult, as the notions of Pareto dominance and optimality, which drive most optimization algorithms, are no more relevant to guide the search in the design space or perform decisions. In this talk, we consider two concepts originated from game theory that offer and attractive perspective in this context: Nash equilibria and Kalai-Smorodinski solutions. We first illustrate how those concepts may find a broad range of applications in engineering and machine learning. However, in a derivative-free, expensive black-box context, very few algorithmic solutions are available to solve game problems. Hence, we propose a novel Gaussian-process based approach for solving games in this context. We follow a classical Bayesian optimization framework, with sequential sampling decisions based on acquisition functions. The relevance of our approach is shown on several problems, including the challenging calibration of an agent-based model with ten objectives.
12h30-14h00 Lunch   
14h00-14h15 Rodolphe Le Riche
 The OQUAIDO research chair in a nutshell 
(abstract) The OQUAIDO research chair aims at gathering academical and technological partners to work on problems involving costly-to-evaluate numerical simulators for uncertainty quantification, optimization and inverse problems. We will show how such collaborative project differs from, and complements, the CNRS Mascot-Num "Groupement De Recherche" (GDR). The talk will be illustrated by an example of Gaussian processes involving both continuous and categorical inputs.
14h15-15h00 Albert Cohen Optimal sampling in weighted least-squares methods. Application to high-dimensional approximation  
(abstract) SlidesLeast squares methods are of common use when one needs to approximate a function based on its noiseless or noisy observation at n scattered points by a simpler function chosen in an m dimensional space with m less than n. Depending on the context, these points may be randomly drawned according to some distribution, or deterministically selected by the user. This talk will survey some recent results on the stability and approximation properties of weighted least squares method, in relation with the spatial distribution of the sampling. One of our main finding is that an optimal random sampling strategy can be defined by means of the Christoffel function associated with the space where the approximation is searched. Here, optimal means that near-best approximation properties are achieved at the prize of a number of sample n larger than m only by a logarithmic factor. One principal motivation is the application to high-dimensional approximation problems, such as coming PDEs with random input parameters. Motivated by this setting, we also discuss how the optimal sampling can be practically generated and incrementally updated when the approximation spaces are adaptively selected..
15h00-15h45 Yohann De Castro Un programme SDP pour résoudre le problème des plans d’expériences optimaux 
(abstract) Dans cet exposé, on rappellera le problème de la construction de plans d’expériences optimaux pour la régression polynomiale multivariée. On présentera un algorithme SDP (calculable en temps polynomial) pour résoudre ce problème. Cet algorithme sera basé sur un outil (la représentation « Sum-Of-Squares ») permettant de minimiser un fonction convexe dont les arguments sont les moments (multivariés) d’une mesure de probabilité.
15h45-16h15 Hervé Monod GDR Mascot-Num Slides
16h15-16h30 Closing remarks  

 

 
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