Events

Robust Estimation under the Wasserstein Distance

Speaker: Sloan Nietert

Location: 60 Fifth Avenue, Room 650

Date: Monday, April 24, 2023

Modern machine learning (ML) and statistics rely on high-dimensional data sets with rich geometric structure. The Wasserstein distance, rooted in optimal transport (OT) theory, compares data distributions while respecting this geometry, and recent computational advances have fueled its widespread adoption for ML tasks. Unfortunately, classic OT suffers from a sensitivity to outliers which precludes meaningful performance guarantees when data is corrupted. In this talk, I will present recent work on the intersection of optimal transport and robust statistics. By combining so-called “partial OT” with the statistical method of minimum distance estimation, we achieve the minimax risk for robust estimation under the Wasserstein metric, and an accompanying duality theory enables applications to robust generative modeling. Finally, we adapt this framework to sliced OT, which considers only low-dimensional projections of the input measures, and demonstrate significant gains in scalability.