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In this 48-minute lecture, Carnegie Mellon University's Sivaraman Balakrishnan presents stability bounds for optimal transport maps and their statistical implications. Recorded at IPAM's Statistical and Numerical Methods for Non-commutative Optimal Transport Workshop on May 22, 2025, the talk explores how stability bounds can reduce the challenge of estimating optimal transport maps to estimating densities in the Wasserstein distance. Discover the consequences of these stability bounds in statistical optimal transport, including methods for estimating OT maps between smooth distributions, log-concave distributions, and moment-bounded distributions from random samples. The presentation draws from joint research with Tudor Manole, Jonathan Niles-Weed, and Larry Wasserman, offering valuable insights for researchers and practitioners in the field of optimal transport theory and its statistical applications.
