7 results on '"Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE ParisTech)"'
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2. Neural networks-based backward scheme for fully nonlinear PDEs
- Author
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Huyên Pham, Maximilien Germain, Xavier Warin, Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université de Paris (UP), Laboratoire de Finance des Marchés d'Energie (FiME Lab), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF)-CREST-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), EDF (EDF), Optimisation, Simulation, Risque et Statistiques pour les Marchés de l’Energie (EDF R&D OSIRIS), EDF (EDF)-EDF (EDF), Université Paris Diderot - Paris 7 (UPD7), Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE ParisTech), Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Université Paris Dauphine-PSL-CREST-EDF R&D (EDF R&D), and Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001))
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FOS: Computer and information sciences ,Hessian matrix ,Automatic differentiation ,MathematicsofComputing_NUMERICALANALYSIS ,fully nonlinear PDEs in high dimension ,Machine Learning (stat.ML) ,[INFO.INFO-NE]Computer Science [cs]/Neural and Evolutionary Computing [cs.NE] ,01 natural sciences ,010305 fluids & plasmas ,symbols.namesake ,Mathematics - Analysis of PDEs ,Dimension (vector space) ,[STAT.ML]Statistics [stat]/Machine Learning [stat.ML] ,Statistics - Machine Learning ,fully nonlinear PDEs in high dimension MSC Classification: 60H35 ,0103 physical sciences ,Deep neural networks ,FOS: Mathematics ,Applied mathematics ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Neural and Evolutionary Computing (cs.NE) ,0101 mathematics ,Mathematics - Optimization and Control ,Mathematics ,Numerical Analysis ,Partial differential equation ,Artificial neural network ,Applied Mathematics ,Numerical analysis ,Probability (math.PR) ,010102 general mathematics ,65M12 ,Computer Science - Neural and Evolutionary Computing ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,Computational Mathematics ,Nonlinear system ,Optimization and Control (math.OC) ,symbols ,65C20 ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,Portfolio optimization ,Analysis ,Mathematics - Probability ,Neural networks ,Analysis of PDEs (math.AP) - Abstract
We propose a numerical method for solving high dimensional fully nonlinear partial differential equations (PDEs). Our algorithm estimates simultaneously by backward time induction the solution and its gradient by multi-layer neural networks, while the Hessian is approximated by automatic differentiation of the gradient at previous step. This methodology extends to the fully nonlinear case the approach recently proposed in \cite{HPW19} for semi-linear PDEs. Numerical tests illustrate the performance and accuracy of our method on several examples in high dimension with nonlinearity on the Hessian term including a linear quadratic control problem with control on the diffusion coefficient, Monge-Amp{\`e}re equation and Hamilton-Jacobi-Bellman equation in portfolio optimization., Comment: to appear in SN Partial Differential Equations and Applications
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- 2020
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3. Fabien Brugière, La sous-traitance en piste. Les ouvriers de l’assistance aéroportuaire
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Lucas Tranchant, Centre d'Economie et de Sociologie Rurales Appliquées à l'Agriculture et aux Espaces Ruraux (CESAER), Institut National de la Recherche Agronomique (INRA)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement, Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE ParisTech), and Etablissement National d'Enseignement Supérieur Agronomique de Dijon (ENESAD)-Institut National de la Recherche Agronomique (INRA)
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[SHS.SOCIO]Humanities and Social Sciences/Sociology ,sous-traitance ,libéralisation - Abstract
Fabien Brugière, La sous-traitance en piste. Les ouvriers de l’assistance aéroportuaire
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- 2018
4. Linear-Quadratic McKean-Vlasov Stochastic Differential Games
- Author
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Miller, Enzo, Pham, Huyen, Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Paris Diderot - Paris 7 (UPD7), Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE ParisTech), This work is supported by FiME (Finance for Energy Market Research Centre) and the ``Finance et D\'eveloppement Durable - Approches Quantitatives' EDF - CACIB Chair., Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)), Laboratoire de Probabilités, Statistique et Modélisation (LPSM UMR 8001), and Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)
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open-loop controls ,Computer Science::Computer Science and Game Theory ,Probability (math.PR) ,Nash equilibria ,[MATH.MATH-PR]Mathematics [math]/Probability [math.PR] ,Optimization and Control (math.OC) ,MSC: 49N10, 49L20, 91A13 ,FOS: Mathematics ,weak martingale optimality principle ,stochastic differential game ,linear-quadratic ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,Mean-field SDEs ,Mathematics - Optimization and Control ,Mathematics - Probability - Abstract
We consider a multi-player stochastic differential game with linear McKean-Vlasov dynamics and quadratic cost functional depending on the variance and mean of the state and control actions of the players in open-loop form. Finite and infinite horizon problems with possibly some random coefficients as well as common noise are addressed. We propose a simple direct approach based on weak martingale optimality principle together with a fixed point argument in the space of controls for solving this game problem. The Nash equilibria are characterized in terms of systems of Riccati ordinary differential equations and linear mean-field backward stochastic differential equations: existence and uniqueness conditions are provided for such systems. Finally, we illustrate our results on a toy example.
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- 2018
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5. Functional Linear Regression with Functional Response
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Jean-Pierre Florens, David Benatia, Marine Carrasco, Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE ParisTech), HEC Montréal (HEC Montréal), Université de Montréal, Départment d'Economie, Centre interuniversitaire de recherche en économie quantitative (CIREQ), Toulouse School of Economics (TSE), Université Toulouse 1 Capitole (UT1), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)
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Economics and Econometrics ,Mathematical optimization ,Functional regression ,Generalization ,Asymptotic distribution ,Instrumental variables ,01 natural sciences ,[SHS]Humanities and Social Sciences ,Tikhonov regularization ,010104 statistics & probability ,symbols.namesake ,Operator (computer programming) ,0502 economics and business ,Linear regression ,Applied mathematics ,[MATH]Mathematics [math] ,0101 mathematics ,B- ECONOMIE ET FINANCE ,050205 econometrics ,Mathematics ,[QFIN]Quantitative Finance [q-fin] ,Applied Mathematics ,05 social sciences ,JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C13 - Estimation: General ,Hilbert space ,Estimator ,[STAT]Statistics [stat] ,Rate of convergence ,Linear operator ,symbols - Abstract
In this paper, we develop new estimation results for functional regressions where both the regressor Z ( t ) and the response Y ( t ) are functions of Hilbert spaces, indexed by the time or a spatial location. The model can be thought as a generalization of the multivariate regression where the regression coefficient is now an unknown operator Π . We propose to estimate the operator Π by Tikhonov regularization, which amounts to apply a penalty on the L 2 norm of Π . We derive the rate of convergence of the mean-square error, the asymptotic distribution of the estimator, and develop tests on Π . As trajectories are often not fully observed, we consider the scenario where the data become more and more frequent (infill asymptotics). We also address the case where Z is endogenous and instrumental variables are used to estimate Π . An application to the electricity consumption completes the paper.
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- 2017
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6. Des musiciens à bonne école: Les pratiques éducatives des classes supérieures au prisme de l’apprentissage enfantin de la musique
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TRANCHANT, Lucas, Centre d'Economie et de Sociologie Rurales Appliquées à l'Agriculture et aux Espaces Ruraux (CESAER), Institut National de la Recherche Agronomique (INRA)-AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement, Laboratoire de sociologie quantitative, and Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE ParisTech)
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Inégalités scolaires ,music learning is sometimes directly included in schooling strategies with the aim of reaching selective schools or classes early on ,Enfance ,Musique ,[SDV]Life Sciences [q-bio] ,Loisirs ,Arts ,at the middle school level. All these elements suggest that the growing schooling competition in the Paris area has an effect on the way in which families invest in children’s leisure activities ,the wish of being a member of the music academy appears as decisive as the desire of playing music. The music academy is a sought-after institution because of its serious and formal pedagogy ,but the mechanisms through which this selectivity works are still to be understood. This study is based on a field research conducted among upper-class families of a gentrified neighborhood in a Paris suburb municipality and on a statistical analysis of t ,Music learning in conservatories is a socially selective organized children’s leisure activity ,and it is seen as fostering the formation of educational aptitudes. Moreover ,Pratiques culturelles ,Éducation ,Pratiques artistiques - Abstract
Si l’apprentissage de la musique en conservatoire est une activité enfantine socialement sélective, les mécanismes par lesquels passe cette sélectivité sont encore mal connus. Une enquête de terrain menée auprès de familles des classes supérieures d’un quartier gentrifié d’une commune de proche banlieue parisienne, ainsi que l’accès aux fichiers administratifs du conservatoire montrent que la musique est une activité socialement et localement distinctive, participant de la formation d’un entre-soi et dirigée vers les normes de légitimité de la culture savante. La volonté d’être au conservatoire apparaît comme aussi déterminante que celle de faire de la musique. Institution recherchée pour son caractère sérieux et scolaire, le conservatoire est perçu comme favorisant la formation de dispositions scolaires. La musique est aussi parfois directement intégrée aux stratégies scolaires pour accéder à des classes sélectives dès le collège. Ces éléments indiquent que le renforcement de la compétition scolaire en région parisienne agit également sur la façon dont sont investies les pratiques de loisirs enfantines.
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- 2016
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7. Posterior concentration rates for empirical Bayes procedures, with applications to Dirichlet Process mixtures
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Vincent Rivoirard, Judith Rousseau, Sophie Donnet, Catia Scricciolo, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS), Mathématiques et Informatique Appliquées (MIA-Paris), AgroParisTech-Institut National de la Recherche Agronomique (INRA), Centre de Recherche en Économie et Statistique (CREST), Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] (ENSAI)-École polytechnique (X)-École Nationale de la Statistique et de l'Administration Économique (ENSAE ParisTech )-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Scienze delle Decision, Bocconi University [Milan, Italy], Institut National de la Recherche Agronomique (INRA)-AgroParisTech, CREST, Ecole Nationale de la Statistique et de l'Administration Economique (ENSAE ParisTech), Department of Economics, Università degli Studi di Verona, Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] (ENSAI)-École polytechnique (X)-École Nationale de la Statistique et de l'Administration Économique (ENSAE Paris)-Centre National de la Recherche Scientifique (CNRS), and University of Verona (UNIVR)
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Statistics and Probability ,FOS: Computer and information sciences ,Gaussian ,Mathematics - Statistics Theory ,Statistics Theory (math.ST) ,Empirical Bayes ,Poisson distribution ,01 natural sciences ,Statistics - Computation ,Dirichlet process mixtures ,010104 statistics & probability ,symbols.namesake ,Bayes' theorem ,[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] ,0502 economics and business ,Statistics ,Prior probability ,FOS: Mathematics ,Applied mathematics ,posterior contraction rates ,0101 mathematics ,Computation (stat.CO) ,050205 econometrics ,Mathematics ,[STAT.AP]Statistics [stat]/Applications [stat.AP] ,Counting process ,05 social sciences ,Multiplicative function ,empirical Bayes ,counting processes ,Aalen model ,3. Good health ,Dirichlet process ,symbols ,posterior concentration rates ,Random variable - Abstract
In this paper we provide general conditions to check on the model and the prior to derive posterior concentration rates for data-dependent priors (or empirical Bayes approaches). We aim at providing conditions that are close to the conditions provided in the seminal paper by Ghosal and van der Vaart (2007a). We then apply the general theorem to two different settings: the estimation of a density using Dirichlet process mixtures of Gaussian random variables with base measure depending on some empirical quantities and the estimation of the intensity of a counting process under the Aalen model. A simulation study for inhomogeneous Poisson processes also illustrates our results. In the former case we also derive some results on the estimation of the mixing density and on the deconvolution problem. In the latter, we provide a general theorem on posterior concentration rates for counting processes with Aalen multiplicative intensity with priors not depending on the data., Comment: With supplementary material
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- 2014
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