Activités scientifiques du département
Le DMA est à la fois un département d'enseignement et un département de recherche. Cette structuration originale vise notamment à mettre très tôt les élèves au plus près de la recherche en train de se faire.
L'essentielle de publications des membres du département, des thèses et des HDR qui y sont soutenues sont disponibles sur le serveur HAL.
28 June 2022 halshs-03708109 publication
4 May 2022 hal-03585067 pré-publication
The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods as well as several important results in the field. The models considered include the McKean-Vlasov diffusion, the mean-field jump models and the Boltzmann models. The first part of this review is an introduction to modelling aspects of stochastic particle systems and to the notion of propagation of chaos. The second part presents concrete applications and a more detailed study of some of the important models in the field.
Louis-Pierre Chaintron, Antoine Diez
5 May 2022 tel-03659503 thèse
This thesis proposes theoretical and numerical contributions to perform machine learning and statistics over the space of probability distributions. In a first part, we introduce a new class of neural network architectures to process probability measures in their Lagrangian form (obtained by sampling) as both inputs and outputs, which is characterized by robustness and universal approximation properties. We show that this framework can be adapted to perform regression on probability measure inputs, with customized invariance requirements, in a way that preserves its robustness and approximation capabilities. This method is proven to be of interest to design expressive, adaptable summaries of datasets referred to as “meta-features”, in the context of automated machine learning. In a second part, we demonstrate that the resort to entropy eases the computation of conditional multivariate quantiles. We introduce the regularized vector quantile regression problem, provide a scalable algorithm to compute multivariate quantiles and show that it benefits from desirable asymptotic properties.
Gwendoline de Bie
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