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Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance
Francis Bach

Sat Dec 09 04:10 PM -- 04:50 PM (PST) @
in Optimal Transport and Machine Learning »

The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the empirical measure obtained fromnindependent samples from μ approaches μ in the Wasserstein distance of any order. We prove sharp asymptotic and finite-sample results for this rate of convergence for general measures on general compact metric spaces. Our finite-sample results show the existence of multi-scale behavior, where measures can exhibit radically different rates of convergence as n grows. See more details in: J. Weed, F. Bach. Sharp asymptotic and finite-sample ratesof convergence of empirical measures in Wasserstein distance. Technical Report, Arxiv-1707.00087, 2017.

Author Information

Francis Bach (Inria)

Francis Bach is a researcher at INRIA, leading since 2011 the SIERRA project-team, which is part of the Computer Science Department at Ecole Normale Supérieure in Paris, France. After completing his Ph.D. in Computer Science at U.C. Berkeley, he spent two years at Ecole des Mines, and joined INRIA and Ecole Normale Supérieure in 2007. He is interested in statistical machine learning, and especially in convex optimization, combinatorial optimization, sparse methods, kernel-based learning, vision and signal processing. He gave numerous courses on optimization in the last few years in summer schools. He has been program co-chair for the International Conference on Machine Learning in 2015.

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