Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

L'optimisation de fonctions convexes lisses dans un cadre stochastique, où seules des estimations bruitées des gradients et des Hessiennes sont disponibles, est un problème classique en statistique computationnelle. Si les méthodes de premier ordre possèdent un faible coût par itération, leur convergence peut s'avérer lente pour les problèmes mal conditionnés.

In this talk, we study notions of distances between graphs and their connections to optimal transport and combinatorial optimization. We focus in particular on graph edit distance and its relation to the Quadratic Assignment Problem (QAP), which provides a natural formulation for graph matching under structural constraints. We then introduce optimal transport-based distances, especially the Wasserstein distance and its extension to metric measure spaces via the Gromov–Wasserstein distance.

This work falls within the field of statistical modeling of extreme values, a fundamental area for the analysis and prediction of rare events with potentially severe consequences in domains such as finance, engineering, and natural risk management. Its main objective is to propose a flexible method for estimating extreme conditional quantiles.

The detection of disruptions in stochastic processes has evolved from early control charts to rigorous optimal stopping frameworks and modern adaptive systems. The classical procedures like CUSUM and Shiryaev’s rule set performance benchmarks and continue to inspire extensions to dependent, high-dimensional, and uncertain settings. The numerous application areas span industry, finance, engineering, cybersecurity, environmental protection, and healthcare, with a particularly significant impact on epidemiological surveillance.

Stochastic gradient algorithms and their variants, such as AdaGrad and ADAM, have been extensively studied in recent years to address large-scale, high-dimensional optimization problems. Most theoretical analyses, however, rely on the assumption that unbiased gradient estimators are available.

TBA