This course provides an overview of key advances in continuous optimization and statistical analysis for machine learning. We review recent learning formulations and models as well as their guarantees
Dans ce cours, nous étudierons les notions fondamentales de l'analyse réelle, ainsi que le calcul différentiel et intégral pour les fonctions réelles d'une variable réelle. ...
This is an introductory course on Elliptic Partial Differential Equations. The course will cover the theory of both classical and generalized (weak) solutions of elliptic PDEs. ...
The first part is devoted to Monge and Kantorovitch problems, discussing the existence and the properties of the optimal plan. The second part introduces the Wasserstein distance on measures and develops applications of optimal transport to PDEs, functiona ...
We will present the theory of PDEs and of transport equations with rough (non Lipschitz) velocity fields, address both the renormalisation theory by DiPerna-Lions-Ambrosio and its quantitative Lagrangian counterpart and show applications to mixing estimate ...
In this course we will focus on stochastic approaches for modelling phenomena taking place in multivariate spaces. Our main focus will be on random field models and on statistical methods for model-based spatial statistics. ...