Poster
in
Workshop: Optimal Transport and Machine Learning
A Central Limit Theorems for Multidimensional Wasserstein Distances
Alberto Gonzalez Sanz · Loubes Jean-Michel · Eustasio Barrio
Abstract:
We present recent approaches to prove the asymptotic behaviour of empirical transport cost, Tc(Pn,Q), under minimal assumptions in high dimension. Centering around its expectation, the weak limit of √n{Tc(Pn,Q)−ETc(Pn,Q)} is Gaussian. Yet, due to the curse of dimensionality, the variable ETc(Pn,Q) can not be exchanged by its population counterpart Tc(P,Q). When P is finitely supported this problem can be solved and the limit becomes the supremum of a centered Gaussian process, which is Gaussian under some additional conditions on the probability Q.
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