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- W2912286675 abstract "The Wasserstein distances are a set of metrics on probability distributionssupported on $mathbb{R}^d$ with applications throughout statistics and machinelearning. Often, such distances are used in the context of variationalproblems, in which the statistician employs in place of an unknown measure aproxy constructed on the basis of independent samples. This raises the basicquestion of how well measures can be approximated in Wasserstein distance.While it is known that an empirical measure comprising i.i.d. samples israte-optimal for general measures, no improved results were known for measurespossessing smooth densities. We prove the first minimax rates for estimation ofsmooth densities for general Wasserstein distances, thereby showing how thecurse of dimensionality can be alleviated for sufficiently regular measures. Wealso show how to construct discretely supported measures, suitable forcomputational purposes, which enjoy improved rates. Our approach is based onnovel bounds between the Wasserstein distances and suitable Besov norms, whichmay be of independent interest." @default.
- W2912286675 created "2019-02-21" @default.
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- W2912286675 date "2019-02-05" @default.
- W2912286675 modified "2023-09-26" @default.
- W2912286675 title "Estimation of smooth densities in Wasserstein distance" @default.
- W2912286675 hasPublicationYear "2019" @default.
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