Séminaire de Statistique

CREST, ENSAE, Université Paris-Saclay

et

CMAP, Ecole Polytechnique

Organisateurs:

 C. Butucea, A. B. Tsybakov, (CREST)

E. Moulines, M. Rosenbaum (CMAP)

 

Sept 2017

Oct 2017

Nov 2017

Déc 2017

Jan 2018

Fév 2018

Mar 2018

Avr 2018

Mai 2018

Juin 2018

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sept 11 2017

Arnak Dalalyan

ENSAE

Title : User-friendly bounds for sampling from a log-concave density using Langevin Monte Carlo

 

Abstract :  We will present new bounds on the sampling error in the case where the target distribution has a smooth and log-concave density. These bounds are established for the Langevin Monte Carlo and its discretized versions involving the Hessian matrix of the log-density. We will also discuss the case where accurate evaluation of the gradient is impossible.

Sept 18 2017

Séminaire Parisien de Statistique - IHP

 

Sept 25 2017

Mathias Trabs

Université de Hamburg

Title : Volatility estimation for stochastic PDE’s using high-frequency observations

 

Abstract : We study the parameter estimation for parabolic, linear, second order, stochastic partial differential equations (SPDEs) observing a mild solution on a discrete grid in time and space. A high-frequency regime is considered where the mesh of the grid in the time variable goes to zero. Focusing on volatility estimation, we provide an explicit and easy to implement method of moments estimator based on the squared increments of the process. The estimator is consistent and admits a central limit theorem. Starting from a representation of the solution as an infinite factor model, the theory considerably differs from the statistics for semi-martingales literature. The performance of the method is illustrated in a simulation study.


This is joint work with Markus Bibinger.

 

 

 

Oct 2 2017

Nicolas Marie

Modal’X (Paris 10)/ ESME Sudria

Title : Estimation non-paramétrique dans les équations différentielles dirigées par le mouvement brownien fractionnaire.

 

Abstract : Après avoir introduit quelques notions de calcul stochastique trajectoriel, l’exposé présentera un estimateur type Nadaraya-Watson de la fonction de drift d’une équation différentielle dirigée par un bruit multiplicatif fractionnaire. Afin d’établir la consistance de l’estimateur, les résultats d’ergodicité de Hairer et Ohashi (2007) seront énoncés et expliqués. Une fois sa consistence établie, la question de la vitesse de convergence de l’estimateur sera abordée. Il s’agit d’un travail en collaboration avec F. Comte.

Oct 9 2017

Zoltan Szabo

Ecole Polytechnique

Title :

 

Abstract :

Oct 16 2017

Séminaire Parisien de Statistique - IHP

 

Oct 23 2017

Philip Thompson

ENSAE

Title : Stochastic approximation with heavier tails

 

Abstract : We consider the solution of convex optimization and variational inequality problems via the stochastic approximation methodology where the gradient or operator can only be accessed through an unbiased stochastic oracle. First, we show that (non-asymptotic) convergence is possible with unbounded constraints and a "multiplicative noise" model: the oracle is Lipschitz continuous with a finite pointwise variance which may not be uniformly bounded (as classically assumed). In this setting, our bounds depend on local variances at solutions and the method uses noise reduction in an efficient manner: given a precision, it respects a near-optimal sample and averaging complexities of Polyak-Ruppert's method but attains the order of the (faster) deterministic iteration complexity. Second, we discuss a more "robust" version where the Lipschitz constant L is unknown but, in terms of error precision, near-optimal complexities are maintained. A price to pay when L is unknown is that a large sample regime is assumed (still respecting the complexity of the SAA estimator) and "non-martingale-like" dependencies are introduced. These dependencies are coped with an "iterative localization" argument based on empirical process theory and self-normalization. 

Joint work with A. Iusem (IMPA), A. Jofré (CMM-Chile) and R.I. Oliveira (IMPA).

Oct 30 2017

Vacances

 

 

 

 

Nov 6 2017

Martin Kroll

ENSAE

Title :

 

Abstract :

Nov 13 2017

Séminaire Parisien de Statistique - IHP

 

Nov 20 2017

Olivier Collier

Université Paris Nanterre

Title :

 

Abstract :

Nov 27 2017

Elisabeth Gassiat

Université Paris-Sud

Title :

 

Abstract :

 

 

 

Dec 4 2017

 

 

Dec 11 2017

 

 

Dec 18 2017

Pas de séminaire

 

 

 

 

Jan 8 2018