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

  title={Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance},
  author={Jonathan Weed and Francis R. Bach},
  • J. WeedF. Bach
  • Published 1 July 2017
  • Mathematics, Computer Science
  • Bernoulli
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 from $n$ independent samples from $\mu$ approaches $\mu$ 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… 

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