Date/Time Date(s) - 17/01/202511:00 am - 12:00 pm
Speaker: Paul Escande
Location: Hamilton Hall, Room 410 / Zoom
Title: On the Concentration of the Minimizers of Empirical Risks
Abstract: Obtaining guarantees on the convergence of the minimizers of empirical risks to the ones of the true risk is a fundamental matter in statistical learning.
Instead of deriving guarantees on the usual estimation error, we will explore concentration inequalities on the distance between the sets of minimizers of the risks. We will argue that for a broad spectrum of estimation problems, there exists a regime where optimal concentration rates can be proven. The bounds will be showcased on a selection of estimation problems such as barycenters on metric space with positive or negative curvature, subspaces of covariance matrices, regression problems and entropic-Wasserstein barycenters.