Approximation by finitely supported measures

By Benoît R. Kloeckner. 2010

65 citations recorded by the source corpus.

We consider the problem of approximating a probability measure defined on a metric space by a measure supported on a finite number of points. More specifically we seek the asymptotic behavior of the minimal Wasserstein distance to an approximation when the number of points goes to infinity. The main result gives an equivalent when the space is a Riemannian manifold and the approximated measure is absolutely continuous and compactly supported.

Subfields: Applied Mathematics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/08285c6cbf4f9ef9705ed670ffeaf671ecee8d4c

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In Applied Mathematics

In Statistical and Nonlinear Physics

In Statistics and Probability

Citations in the corpus

Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance (2017, background): “That such lower bounds are often tight for empirical measures is a rather surprising fact, which has been noted several times, including in Dudley’s original paper [7,10,16,18,28].”
Stochastic Wasserstein Barycenters (2018, unknown): “The following theoretical result shows that the use of uniform measures supported on a finite set of points can approximate the barycenter arbitrarily well: Theorem (Metric convergence, Kloeckner (2012); Brancolini et al. (2009)).”