Jose Blanchet
On Wasserstein projections
We study the minimum Wasserstein distance from the empirical measure to a space of probability measures satisfying linear constraints. This statistic can naturally be used in a wide range of applications, for example, optimally choosing uncertainty sizes in distributionally robust optimization, optimal regularization, testing fairness, martingality, among many other statistical properties. We will discuss duality results which recover the celebrated Kantorovich-Rubinstein duality when the manifold is sufficiently rich and associated test statistics as the sample size increases. We illustrate how this relaxation can beat the statistical curse of dimensionality often associated to empirical Wasserstein distances.
The talk builds on joint work with S. Ghosh, Y. Kang, K. Murthy, M. Squillante, and N. Si.
Our speaker
Jose Blanchet is a Professor in the Management Science and Engineering Department at Stanford University – where he earned his Ph.D. in 2004. Prior to joining the Stanford faculty, Jose was a Professor in the IEOR and Statistics Departments at Columbia University (2008-2017) and before that he was faculty member in the Statistics Department at Harvard University (2004-2008). Jose is a recipient of the Erlang Prize and the Best Publication Award given by the INFORMS Applied Probability Society. He also received a PECASE award given by the White House. He has research interests in applied probability, stochastic optimization, and Monte Carlo methods. He is an Area Editor of Mathematics of Operations Research and serves on the board of Advances in Applied Probability, Extremes, Insurance: Mathematics and Economics, Journal of Applied Probability and Stochastic Systems.
