Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

Dans ce travail, nous étudions un modèle de régression visant à décrire le comportement des valeurs extrêmes d’une variable Y à partir de covariables X. Nous proposons une méthode de réduction de dimension spécialement conçue pour les queues de distribution, permettant de surmonter le fléau de la grande dimension et d’améliorer l’estimation de l’indice des valeurs extrêmes conditionnel.

TBA

Le schéma JKO (pour Jordan, Kinderlehrer, Otto, 1996) est un schéma de 
type Euler implicite permettant de construire de façon variationnelle 
des solutions faibles d'équations de diffusion non-linéaire en 
s'appuyant sur leur structure de flot de gradient dans l'espace de 
Wasserstein. En 2015, Peyré en a proposé une version nommée entropique 
qui, bien que ne fournissant que des solutions approchées du problème 
originel, donne lieu à des calculs numériques redoutablement efficaces, 

Stochastic Newton methods capable of achieving asymptotic efficiency have historically required a per-iteration cost of O(d3) for problems of dimension d. This presentation will first review the concept of asymptotic efficiency, the statistical benchmark for an optimal estimator. We then introduce an online algorithm that achieves this same statistical optimality with a reduced per-iteration cost of O(ℓd2), where the mask size ℓ can be chosen

The Boolean model of random covering was introduced by Gilbert in the 1960s as a simplified representation of a radio transmission network [2]. It is obtained by considering the union of balls of fixed radius centered at the points of a homogeneous Poisson point process in Euclidean space.

« Micro-swimming », the study of locomotion at microscopic scale, is a broad topic with applications ranging from biology to medical robotics. The locomotion problem may be modelled as a nonlinear control-affine system, with or without a drift depending on modeling assumptions, such as environment model and the way deformation is controlled. This raises the question of controllability, i.e. the ability of the locomotor to reach any desired state.

Stochastic Newton methods capable of achieving asymptotic efficiency have historically required a per-iteration cost of O(d3) for problems of dimension d. This presentation will first review the concept of asymptotic efficiency, the statistical benchmark for an optimal estimator. We then introduce an online algorithm that achieves this same statistical optimality with a reduced per-iteration cost of O(ℓd2), where the mask size ℓ can be chosen