- data e orario: 9 Aprile 2024 ore 14.30
- sala riunioni primo piano, campus Perrone, via Perrone, 18, Novara. Università del Piemonte Orientale.
- on-line: meet.google.com/isi-ipsn-tpa

Title: From Monge to Huber through a Schrödinger Bridge: Robust Optimal Transport in Large Dimensions
Prof. Davide La Vecchia, University of Geneva

Abstract: Optimal Transport (OT) plays an increasingly important role in modern statistics and machine learning. I will begin the talk with a gentle introduction to the OT problem, first in its classical Monge formulation andthen in the relaxed Kantorovich framework, highlighting their statistical relevance and limitations. I will then present two recent advances that address the sensitivity of classical OT to outliers and heavy-tailed distributions. The first is the Robust Optimal Transport (ROBOT) framework, which leads to the robust Wasserstein Distance , a Huberised version of . I discuss its main properties,concentration inequalities, and consequences for minimum-distance estimation,together with applications in statistics (e.g., location estimation under heavy tails) and in machine learning (e.g., Generative Adversarial Networks). I will illustrate that ROBOT is effective in handling outlying values but is still sensitive to the dimensionality of the data. Thus, in the second part of the talk I introduce E-ROBOT, which integrates ROBOT with entropic regularization through connections to the Schrödinger bridge problem. This yields the robust Sinkhorn divergence , which enjoys dimension-free sample complexity of order, where n denotes the sample size. I briefly illustrate its use in large dimensional tasks in statistics, image analysis, and machine learning (e.g., goodness-of-fit testing, barycenter computation for corrupted shapes, gradient flows, and image colour transfer).  Overall, the talk provides a unified perspective on robustness and regularization in OT, together with theoretical guarantees and practical computational tools.