Talk Information 03/24/2022

Abstract: The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and demonstrated utility, Wasserstein distances are sensitive to outliers in the considered distributions, which hinders applicability in practice. We propose a new outlier-robust Wasserstein distance Wₚᵋ which allows for ε outlier mass to be removed from each contaminated distribution. Under standard moment assumptions, Wₚᵋ is shown to be minimax optimal for robust estimation under adversarial contaminations. Our formulation of this robust distance amounts to a highly regular optimization problem that lends itself better for analysis compared to previously considered frameworks. Leveraging this, we conduct a thorough theoretical study of Wₚᵋ, encompassing robustness guarantees, characterization of optimal perturbations, regularity, duality, and statistical estimation. In particular, by decoupling optimization variables, we arrive at a simple dual form for Wₚᵋ that can be implemented via an elementary modification to standard, duality-based OT solvers. We illustrate the virtues of our framework via applications to generative modeling with contaminated datasets. 

Bio: Sloan Nietert is a third-year PhD student in Computer Science at Cornell University, where he is advised by Ziv Goldfeld. His research interests include learning theory, algorithms, and statistics in high dimensions, with a particular focus on optimal transport. His honors include the NSF Graduate Research Fellowship, a Fulbright U.S. Student Grant with the Alfréd Rényi Institute of Mathematics, and the Outstanding Senior in Science award from Clemson University.