Gaussian approximation for empirical barycenters

04/01/2019

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by   Nazar Buzun, et al.

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In this work we consider Wasserstein barycenters (average in Wasserstein distance) in Fourier basis. It includes a provement that a random Fourier parameter of the barycenter is close to a Gaussian random vector by distribution. The convergence rate is O(p/√(n)) depending on measures count (n) and the dimension of parameter (p).