Publications

2017

• Algorithmes Gradient-Proximaux Stochastiques
  
  • Fort Gersende
  • Risser Laurent
  • Moulines Éric
  • Ollier Edouard
  • Samson Adeline
  , 2017. Motivés par des applications en inférence statistique, nous proposons deux versions stochastiques de l'algorithme Gradient Proximal pour la maximisation de fonctions composites. Nous établissons la convergence dans le cas concave, lorsque les approximations Monte Carlo sont biaisées avec un biais qui ne s'atténue pas au cours des itérations.
• Méthode de Monte Carlo à dynamique hamiltonienne pour estimation d'un modèle thermique de bâtiment
  
  • Nabil Tahar
  • Moulines Eric
  • Jicquel Jean-Marc
  • Girard Alexandre
  • Lajaunie Christian
  , 2017.
• A synoptic approach to the seismic sensing of heterogeneous fractures: from geometric reconstruction to interfacial characterization
  
  • Pourahmadian Fatemeh
  • Guzina Bojan B
  • Haddar Houssem
  Computer Methods in Applied Mechanics and Engineering, Elsevier, 2017, 324, pp.395-412. A non-iterative waveform sensing approach is proposed toward (i) geometric reconstruction of penetrable fractures, and (ii) quantitative identification of their heterogeneous contact condition by seismic i.e. elastic waves. To this end, the fracture support Γ (which may be non-planar and unconnected) is first recovered without prior knowledge of the interfacial condition by way of the recently established approaches to non-iterative waveform tomography of heterogeneous fractures, e.g. the methods of generalized linear sampling and topological sensitivity. Given suitable approximation ˘ Γ of the fracture geometry, the jump in the displacement field across ˘ Γ i.e. the fracture opening displacement (FOD) profile is computed from remote sensory data via a regularized inversion of the boundary integral representation mapping the FOD to remote observations of the scattered field. Thus obtained FOD is then used as input for solving the traction boundary integral equation on ˘ Γ for the unknown (linearized) contact parameters. In this study, linear and possibly dissipative interactions between the two faces of a fracture are parameterized in terms of a symmetric, complex-valued matrix K(ξ) collecting the normal, shear, and mixed-mode coefficients of specific stiffness. To facilitate the high-fidelity inversion for K(ξ), a 3-step regularization algorithm is devised to minimize the errors stemming from the inexact geometric reconstruction and FOD recovery. The performance of the inverse solution is illustrated by a set of numerical experiments where a cylindrical fracture, endowed with two example patterns of specific stiffness coefficients, is illuminated by plane waves and reconstructed in terms of its geometry and heterogeneous (dissipative) contact condition. (10.1016/j.cma.2017.06.002)
  DOI : 10.1016/j.cma.2017.06.002
• Queuing for an infinite bus line and aging branching process
  
  • Bansaye Vincent
  • Camanes Alain
  , 2017. We study a queueing system with Poisson arrivals on a bus line indexed by integers. The buses move at constant speed to the right and the time of service per customer getting on the bus is fixed. The customers arriving at station i wait for a bus if this latter is less than d_i stations before, where d_i is non-decreasing. We determine the asymptotic behavior of a single bus and when two buses eventually coalesce almost surely by coupling arguments. Three regimes appear, two of which leading to a.s. coalescing of the buses. The approach relies on a connection with aged structured branching processes with immigration and varying environment. We need to prove a Kesten Stigum type theorem, i.e. the a.s. convergence of the successive size of the branching process normalized by its mean. The technics developed combines a spine approach for multitype branching process in varying environment and geometric ergodicity along the spine to control the increments of the normalized process.
• Aircraft Dynamics Identification
  
  • Rommel Cédric
  • Bonnans Joseph Frédéric
  • Gregorutti Baptiste
  • Martinon Pierre
  , 2017.
• Décomposition de domaine avec multipréconditionnement adaptatif pour les calculs de structure
  
  • Gosselet Pierre
  • Bovet Christophe
  • Parret-Fréaud Augustin
  • Spillane Nicole
  , 2017. Les méthodes de décomposition de domaine permettent de définir des préconditionneurs parallèles performants pour le calcul de structure. Parmi ces méthodes, citons FETI(DP), BDD(C), latin ou RAS. Ces préconditionneurs incorporent une composante multiéchelle (généralement appelée grille grossière ou problème macroscopique) pour transmettre les effets à grande longueur d'onde (principe de Saint-Venant). Récemment il a été compris que certaines situations (hétérogénéités, géométrie irrégulière aux interfaces) étaient susceptibles de générer des phénomènes locaux qui se repercutaient sur l'ensemble de la structure et pénalisaient fortement la résolution. Pour remédier à ce problème de techniques de détection préalable de ces difficultés sont possibles via des analyses aux valeurs propres généralisées localisées (GENEO, deluxe scaling, adaptive FETIDP), suivies par des méthodes d'augmentation pour ne pas les activer au cours de la résolution. L'alternative étudiée ici consiste à tenter de détecter et éliminer au cours de la résolution les phénomènes néfastes à la résolution. Cette technique prend la forme d'un multipréconditionnement : à chaque itération, les contributions des sous-domaines calculées en parallèle sont recombinées de manière optimale. Cette technique a l'avantage de pouvoir fonctionner sur des problèmes autres que symétriques définis positifs. Malheureusement, le coût numérique associé croît relativement rapidement avec le nombre de sous-domaines. On étudie ici diverses techniques d'adaptation de ces techniques multipréconditionnées pour être capable de mener des calculs à plusieurs milliers de sous-domaines : critères de sélection des directions de recherche, et regroupement des directions de recherches par agrégats connexes de sous-domaines. Les méthodes seront illustrées sur des calculs de complexité industrielle conduits sur des clusters de plusieurs milleirs de coeurs. Ces travaux sont en partie financés par l'Agence Nationale de la Recherche dans le cadre du projet SEMAFOR ( ANR-14-CE07-0037)
• Demand Side Management in the Smart Grid: an Efficiency and Fairness Tradeoff
  
  • Jacquot Paulin
  • Beaude Olivier
  • Gaubert Stéphane
  • Oudjane Nadia
  , 2017. We compare two Demand Side Management (DSM) mechanisms, introduced respectively by Mohsenian-Rad et al (2010) and Baharlouei et al (2012), in terms of efficiency and fairness. Each mechanism defines a game where the consumers optimize their flexible consumption to reduce their electricity bills. Mohsenian-Rad et al propose a daily mechanism for which they prove the social optimality. Baharlouei et al propose a hourly billing mechanism for which we give theoretical results: we prove the uniqueness of an equilibrium in the associated game and give an upper bound on its price of anarchy. We evaluate numerically the two mechanisms, using real consumption data from Pecan Street Inc. The simulations show that the equilibrium reached with the hourly mechanism is socially optimal up to 0.1%, and that it achieves an important fairness property according to a quantitative indicator we define. We observe that the two DSM mechanisms avoid the synchronization effect induced by non- game theoretic mechanisms, e.g. Peak/OffPeak hours contracts. (10.1109/ISGTEurope.2017.8260265)
  DOI : 10.1109/ISGTEurope.2017.8260265
• A RESHETNYAK-TYPE LOWER SEMICONTINUITY RESULT FOR LINEARISED ELASTO-PLASTICITY COUPLED WITH DAMAGE IN $W^1,n$
  
  • Crismale Vito
  • Orlando Gianluca
  , 2017. In this paper we prove a lower semicontinuity result of Reshetnyak type for a class of functionals which appear in models for small-strain elasto-plasticity coupled with damage. To do so we characterise the limit of measures $\alpha_k \mathrm{E}u_k$ with respect to the weak convergence $\alpha_k \rightharpoonup \alpha$ in $W^1,n(\Omega)$ and the weak$^*$ convergence $u_k \rightharpoonup^* u$ in $BD(\Omega)$ , $\mathrm{E}$ denoting the symmetrised gradient. A concentration compactness argument shows that the limit has the form $\alpha \mathrm{E}u + \eta$, with $\eta$ supported on an at most countable set.
• An Adaptive Test of Independence with Analytic Kernel Embeddings
  
  • Jitkrittum Wittawat
  • Szabó Zoltán
  • Gretton Arthur
  , 2016, 70, pp.1742-1751. A new computationally efficient dependence measure, and an adaptive statistical test of independence, are proposed. The dependence measure is the difference between analytic embeddings of the joint distribution and the product of the marginals, evaluated at a finite set of locations (features). These features are chosen so as to maximize a lower bound on the test power, resulting in a test that is data-efficient, and that runs in linear time (with respect to the sample size n). The optimized features can be interpreted as evidence to reject the null hypothesis, indicating regions in the joint domain where the joint distribution and the product of the marginals differ most. Consistency of the independence test is established, for an appropriate choice of features. In real-world benchmarks , independence tests using the optimized features perform comparably to the state-of-the-art quadratic-time HSIC test, and outperform competing O(n) and O(n log n) tests.
• Stationary solutions of discrete and continuous Petri nets with priorities
  
  • Allamigeon Xavier
  • Boeuf Vianney
  • Gaubert Stephane
  Performance Evaluation, Elsevier, 2017, 113, pp.1 - 12. We study a continuous dynamics for a class of Petri nets which allows the routing at non-free choice places to be determined by priorities rules. We show that this dynamics can be written in terms of policies which identify the bottleneck places. We characterize the stationary solutions, and show that they coincide with the stationary solutions of the discrete dynamics of this class of Petri nets. We provide numerical experiments on a case study of an emergency call center, indicating that pathologies of discrete models (oscillations around a limit different from the stationary limit) vanish by passing to continuous Petri nets. (10.1016/j.peva.2017.04.007)
  DOI : 10.1016/j.peva.2017.04.007
• Origins of spectral broadening of incoherent waves: Catastrophic process of coherence degradation
  
  • Xu G.
  • Garnier Josselin
  • Rumpf B.
  • Fusaro A.
  • Suret P.
  • Randoux S.
  • Kudlinski Alexandre
  • Millot G.
  • Picozzi A.
  Physical Review A : Atomic, molecular, and optical physics [1990-2015], American Physical Society, 2017, 96 (2). (10.1103/PhysRevA.96.023817)
  DOI : 10.1103/PhysRevA.96.023817
• Cleaning the correlation matrix with a denoising autoencoder
  
  • Hayou Soufiane
  , 2017. In this paper, we use an adjusted autoencoder to estimate the true eigenvalues of the population correlation matrix from a noisy sample correlation matrix when the number of samples is small. We show that the model outperforms the Rotational Invariant Estimator which is the optimal estimator in the sample eigenvectors basis when the dimension goes to infinity.
• Tropical Spectrahedra
  
  • Allamigeon Xavier
  • Gaubert Stephane
  • Skomra Mateusz
  , 2017.
• A tropical approach to bilevel programming: application to a price incentives model in mobile data networks
  
  • Akian Marianne
  • Bouhtou Mustapha
  • Eytard Jean Bernard
  • Gaubert Stephane
  , 2017.
• Computing and Processing Correspondences with Functional Maps
  
  • Ovsjanikov Maks
  • Corman Etienne
  • Bronstein Michael
  • Rodola Emanuele
  • Ben-Chen Mirela
  • Guibas Leonidas
  • Chazal Frédéric
  • Bronstein Alex
  , 2017, pp.1-62. Notions of similarity and correspondence between geometric shapes and images are central to many tasks in geometry processing, computer vision, and computer graphics. The goal of this course is to familiarize the audience with a set of recent techniques that greatly facilitate the computation of mappings or correspondences between geometric datasets, such as 3D shapes or 2D images by formulating them as mappings between functions rather than points or triangles. Methods based on the functional map framework have recently led to state-of-the-art results in problems as diverse as non-rigid shape matching, image co-segmentation and even some aspects of tangent vector field design. One challenge in adopting these methods in practice, however, is that their exposition often assumes a significant amount of background in geometry processing, spectral methods and functional analysis, which can make it difficult to gain an intuition about their performance or about their applicability to real-life problems. In this course, we try to provide all the tools necessary to appreciate and use these techniques, while assuming very little background knowledge. We also give a unifying treatment of these techniques, which may be difficult to extract from the individual publications and, at the same time, hint at the generality of this point of view, which can help tackle many problems in the analysis and creation of visual content. This course is structured as a half day course. We will assume that the participants have knowledge of basic linear algebra and some knowledge of differential geometry, to the extent of being familiar with the concepts of a manifold and a tangent vector space. We will discuss in detail the functional approach to finding correspondences between non-rigid shapes, the design and analysis of tangent vector fields on surfaces, consistent map estimation in networks of shapes and applications to shape and image segmentation, shape variability analysis, and other areas.
• Particle rejuvenation of Rao-Blackwellized Sequential Monte Carlo smoothers for Conditionally Linear and Gaussian models
  
  • Nguyen Ngoc Minh
  • Le Corff Sylvain
  • Moulines Éric
  EURASIP Journal on Advances in Signal Processing, SpringerOpen, 2017, 54. This paper focuses on Sequential Monte Carlo approximations of smoothing distributions in conditionally linear and Gaussian state spaces. To reduce Monte Carlo variance of smoothers, it is typical in these models to use Rao-Blackwellization: particle approximation is used to sample sequences of hidden regimes while the Gaussian states are explicitly integrated conditional on the sequence of regimes and observations, using variants of the Kalman filter / smoother. The first successful attempt to use Rao-Blackwellization for smoothing extends the Bryson-Frazier smoother for Gaussian linear state space models using the generalized two-filter formula together with Kalman filters / smoothers. More recently, a forward backward decomposition of smoothing distributions mimicking the Rauch-Tung-Striebel smoother for the regimes combined with backward Kalman updates has been introduced. This paper investigates the benefit of introducing additional rejuvenation steps in all these algorithms to sample at each time instant new regimes conditional on the forward and backward particles. This defines particle based approximations of the smoothing distributions whose support is not restricted to the set of particles sampled in the forward or backward filter. These procedures are applied to commodity markets which are described using a two factor model based on the spot price and a convenience yield for crude oil data. (10.1186/s13634-017-0489-5)
  DOI : 10.1186/s13634-017-0489-5
• Calibration and prediction of two nested computer codes
  
  • Marque-Pucheu Sophie
  • Perrin Guillaume
  • Garnier Josselin
  , 2017. Thanks to computing power increase, risk quantification relies more and more on computer modeling. Methods of risk quantification based on a fixed computational budget exist, but computer codes are almost always considered as a single black box. In this paper, we are interested in analyzing the behavior of a complex phenomenon, which consists of two nested computer codes. By two nested computer codes, we mean that some inputs of the second code are outputs of the first code. Each code can be approximated by a parametrized computer model. First we propose methods to calibrate the parameters of the computer models and build a pre-dictor of the nested phenomenon for a given set of observations. The presented methods enable to take into account observations of the first code, the second code and the nested code. Second the choice of the observations is studied. Methods of sequential designs, that means step by step addition of observation points to the observations' set, are examined. These sequential designs aim at improving the performance of calibration or prediction while optimizing the computational budget. We show that the independent calibration of the 2 computer models is not efficient for predicting the nested phenomenon. We propose an original method that significantly improves the prediction's performance.
• Per instance algorithm configuration of CMA-ES with limited budget
  
  • Belkhir Nacim
  • Dreo Johann
  • Savéant Pierre
  • Schoenauer Marc
  , 2017, pp.681-688. Per Instance Algorithm Configuration (PIAC) relies on features that describe problem instances. It builds an Empirical Performance Model (EPM) from a training set made of (instance, parameter configuration) pairs together with the corresponding performance of the algorithm at hand. This paper presents a case study in the continuous black-box optimization domain, using features proposed in the literature. The target algorithm is CMA-ES, and three of its hyper-parameters. Special care is taken to the computational cost of the features. The EPM is learned on the BBOB benchmark, but tested on independent test functions gathered from the optimization literature.The results demonstrate that the proposed approach can outperform the default setting of CMA-ES with as few as 30 or 50 time the problem dimension additional function evaluations for feature computation.
• About Some Boundary Integral Operators on the Unit Disk Related to the Laplace Equation
  
  • Ramaciotti Pedro
  • Nédélec Jean-Claude
  SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2017, 55 (4), pp.1892 - 1914. We introduce four integral operators related to the Laplace equation in three dimensions on the circular unit disk. Two of them are related to the weakly singular operator and the other two are related to the hypersingular operator. We provide series expressions for their kernels using proposed bases for the Sobolev trace spaces involved in the symmetric Dirichlet and antisymmetric Neumann Laplace screen problems on the disk. We then provide explicit and closed variational forms suitable for boundary element computations. We develop numerical computation schemes for the associated Galerkin matrices and test their use as preconditioners for the matrices arising from the integral equations associated with the solution of the mentioned screen problems. (10.1137/15M1033721)
  DOI : 10.1137/15M1033721
• A tropical isoperimetric inequality
  
  • Gaubert Stéphane
  • Joswig Michael
  • Jules Depersin
  , 2017, 78B, pp.Article #27. We introduce tropical analogues of the notion of volume of polytopes, leading to a tropical version of the (discrete) classical isoperimetric inequality. The planar case is elementary, but a higher-dimensional generalization leads to an interesting class of ordinary convex polytopes, characterizing the equality case in the isoperimetric inequality. This study is motivated by open complexity questions concerning linear optimization and its tropical analogs.
• Sparse Stochastic Bandits
  
  • Kwon Joon
  • Perchet Vianney
  • Vernade Claire
  , 2017. In the classical multi-armed bandit problem, d arms are available to the decision maker who pulls them sequentially in order to maximize his cumulative reward. Guarantees can be obtained on a relative quantity called regret, which scales linearly with d (or with sqrt(d) in the minimax sense). We here consider the sparse case of this classical problem in the sense that only a small number of arms, namely s < d, have a positive expected reward. We are able to leverage this additional assumption to provide an algorithm whose regret scales with s instead of d. Moreover, we prove that this algorithm is optimal by providing a matching lower bound - at least for a wide and pertinent range of parameters that we determine - and by evaluating its performance on simulated data.
• Computational study of aluminum droplet combustion in different atmospheres
  
  • Muller Mathieu
  • Davidenko Dmitry
  • Giovangigli Vincent
  , 2017, pp.174. Combustion of a single aluminum droplet in different atmospheres is simulated using a 1D approach, recently developed at ONERA, with detailed models for the gas-phase and surface chemistry as well as molecular transport. The reacting flow around a droplet is treated as spherically symmetric and quasi-steady-state by assuming that the droplet regression is slow with respect to the convective and diffusive transport in the surrounding gases. The 1D combustion model is first validated with respect to the 2D axisymmetric approach. It is demonstrated that with the 1D approach, it is possible to take into account the effect of oxidizer convection and obtain parameter profiles closely corresponding to the 2D results. The results of both simulations are found in good agreement with available experimental data for an O2/Ar atmosphere. Using the 1D approach, an important parametric study has been conducted by simulating steady combustion of droplets with different diameters D ≤ 400 µm in three atmospheres (O2/Ar, pure H2O and CO2) at two pressure levels (1 and 10 atm). Effects due to the surface chemistry model and the reversibility of the gas-phase reactions producing Al2O3(L) have been investigated. The burning time and exponent of the law are evaluated for the considered physical conditions and modeling options. Profiles of temperature and mole fractions of important species are presented and analyzed. (10.13009/EUCASS2017-174)
  DOI : 10.13009/EUCASS2017-174
• Aircraft Dynamics Identification for Optimal Control
  
  • Rommel Cédric
  • Bonnans Joseph Frédéric
  • Gregorutti Baptiste
  • Martinon Pierre
  , 2017. Four new Maximum Likelihood based approaches for aircraft dynamics identification are presented and compared. The motivation is the need of accurate dynamic models for minimizing aircraft fuel consumption using optimal control techniques. A robust method for building aerodynamic models is also suggested. All these approaches were validated using real flight data from 25 different aircraft. (10.13009/EUCASS2017-179)
  DOI : 10.13009/EUCASS2017-179
• Some stochastic models for structured populations : scaling limits and long time behavior
  
  • Bansaye Vincent
  • Méléard Sylvie
  , 2017. The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales may lead to different qualitative approximations, either ODEs or SDEs. The prototypes of these equations are the logistic (deterministic) equation and the logistic Feller diffusion process. The convergence in law of the sequence of processes is proved by tightness-uniqueness argument. In these large population approximations, the competition between individuals leads to nonlinear drift terms. We then focus on models without interaction but including exceptional events due either to demographic stochasticity or to environmental stochasticity. In the first case, an individual may have a large number of offspring and we introduce the class of continuous state branching processes. In the second case, catastrophes may occur and kill a random fraction of the population and the process enjoys a quenched branching property. We emphasize on the study of the Laplace transform, which allows us to classify the long time behavior of these processes. In the second chapter, we model structured populations by measure-valued stochastic differential equations. Our approach is based on the individual dynamics. The individuals are characterized by parameters which have an influence on their survival or reproduction ability. Some of these parameters can be genetic and are inheritable except when mutations occur, but they can also be a space location or a quantity of parasites. The individuals compete for resources or other environmental constraints. We describe the population by a point measure-valued Markov process. We study macroscopic approximations of this process depending on the interplay between different scalings and obtain in the limit either integro-differential equations or reaction-diffusion equations or nonlinear super-processes. In each case, we insist on the specific techniques for the proof of convergence and for the study of the limiting model. The limiting processes offer different models of mutation-selection dynamics. Then, we study two-level models motivated by cell division dynamics, where the cell population is discrete and characterized by a trait, which may be continuous. In 1 particular, we finely study a process for parasite infection and the trait is the parasite load. The latter grows following a Feller diffusion and is randomly shared in the two daughter cells when the cell divides. Finally, we focus on the neutral case when the rate of division of cells is constant but the trait evolves following a general Markov process and may split in a random number of cells. The long time behavior of the structured population is then linked and derived from the behavior a well chosen SDE (monotype population).
• Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models
  
  • Douc Randal
  • Fokianos Konstantinos
  • Moulines Éric
  Electronic Journal of Statistics, Shaker Heights, OH : Institute of Mathematical Statistics, 2017, 11 (2), pp.2707 - 2740. We study a general class of quasi-maximum likelihood estimators for observation-driven time series models. Our main focus is on models related to the exponential family of distributions like Poisson based models for count time series or duration models. However, the proposed approach is more general and covers a variety of time series models including the ordinary GARCH model which has been studied extensively in the literature. We provide general conditions under which quasi-maximum likelihood estimators can be analyzed for this class of time series models and we prove that these estimators are consistent and asymptotically normally distributed regardless of the true data generating process. We illustrate our results using classical examples of quasi-maximum likelihood estimation including standard GARCH models, duration models, Poisson type autoregressions and ARMA models with GARCH errors. Our contribution unifies the existing theory and gives conditions for proving consistency and asymptotic normality in a variety of situations (10.1214/17-EJS1299)
  DOI : 10.1214/17-EJS1299