I teach two courses combining mathematical foundations with computational practice.
This second-year ENS course is taught by Samuel Boïté, Julie Delon, Gabriel Peyré and Irène Waldspurger. It introduces the mathematical and numerical tools used throughout modern data science and machine learning.
The course moves from information theory, Fourier analysis and filtering to inverse problems, optimization, machine learning, sampling and generative models. Lectures are complemented by mathematical exercises and numerical experiments in Python.
This Master 2 MVA course is taught by Julie Delon and Gabriel Peyré. It develops optimal transport as a mathematical framework for comparing and evolving probability distributions, with an emphasis on its computational tools and applications to machine learning.
Topics include the Monge and Kantorovich formulations, Wasserstein distances, dual and dynamic formulations, sliced optimal transport, entropic regularization and the Sinkhorn algorithm, as well as gradient flows and generative models. The course combines mathematical lectures, exercises and numerical work in Python.