The theory of optimal transport and the use of Wasserstein distances are attracting increasing attention in statistics and machine learning. At the same time, the definition of sensitivity measures for multivariate responses is a topical research subject. This work examines the construction of probabilistic sensitivity measures using the theory of optimal transport. We obtain a new family of indicators that can deal with multivariate outputs. We test estimators based on alternative algorithmic approaches for computing optimal transport problems, showing promising results and fast execution times for resonable sample sizes.

Joint work with E. Borgonovo & G. Savarè (Bocconi Univ.), A. Figalli (ETH Zürich)