Datalab Seminar
Recent Advances in Optimal Transport Based Inference
Speaker: Eustasio del Barrio (IMUVa, Universidad de Valladolid)Date: Thursday, 20 February 2025 - 12:00Place: Aula Gris 3, ICMAT
Abstract:
Optimal transport has proven to be an important tool to compare probability measures since it enables to define a metric over the set of distributions which conveys their geometric properties. One of the central objects in the theory of optimal transport is the optimal transport (OT) map: the unique monotone transformation pushing forward an absolutely continuous probability law onto any other given law. OT maps play an important role in some recent statistical applications, either as a tool for defining multivariate analogues of quantile functions, for correcting distributional shifts in classification problems or in statistical inference over the space of probability measures. While, from the point of view of minimax rates, estimation of OT maps is affected by the curse of dimensionality, efficient estimation is possible in some interesting setups. In this talk we will present the case of entropic optimal transport and that of semidiscrete optimal transport. We will illustrate the applicability of the results in the estimation of Laguerre cells and in Hotelling’s location model for equillibrium prices.
