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Conference Papers Year : 2021

A Dimension-free Computational Upper-bound for Smooth Optimal Transport Estimation

Abstract

It is well-known that plug-in statistical estimation of optimal transport suffers from the curse of dimensionality. Despite recent efforts to improve the rate of estimation with the smoothness of the problem, the computational complexity of these recently proposed methods still degrade exponentially with the dimension. In this paper, thanks to an infinitedimensional sum-of-squares representation, we derive a statistical estimator of smooth optimal transport which achieves a precision ε fromÕ(ε −2) independent and identically distributed samples from the distributions, for a computational cost ofÕ(ε −4) when the smoothness increases, hence yielding dimension-free statistical and computational rates, with potentially exponentially dimension-dependent constants.
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Dates and versions

hal-03454237 , version 1 (29-11-2021)

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Adrien Vacher, Boris Muzellec, Alessandro Rudi, Francis Bach, François-Xavier Vialard. A Dimension-free Computational Upper-bound for Smooth Optimal Transport Estimation. COLT 2021 - 34th Annual Conference on Learning Theory, Aug 2021, Boulder, United States. ⟨hal-03454237⟩
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