A0190
Title: Some aspects of robust optimal transportation, with applications to statistics and machine learning
Authors: Davide La Vecchia - University of Geneva (Switzerland) [presenting]
Abstract: Optimal transport (OT) theory and the related p-Wasserstein (Wp) distance are popular tools in statistics and machine learning. Recent studies have been remarking that inference based on OT and on Wpis sensitive to outliers. To cope with this issue, we work on a robust version of the primal OT problem (ROBOT) and show that it defines a robust version of W1, called robust Wasserstein distance, which is able to down-weight the impact of outliers. We study the properties of this novel distance and use it to define minimum distance estimators. Our novel estimators do not impose any moment restrictions: this allows us to extend the use of OT methods to inference on heavy-tailed distributions. We also provide statistical guarantees of the proposed estimators. Moreover, we derive the dual form of the ROBOT and illustrate its applicability to machine learning. Numerical exercises provide evidence of the benefits yielded by our methods.
