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Gaussian Approximation for Penalized Wasserstein Barycenters
In this work we consider regularized Wasserstein barycenters (average in Wasserstein distance) in Fourier basis. We prove that random Fourier parameters of the barycenter converge to some Gaussian random vector in distribution. The convergence rate has been derived in finite-sample case with explicit dependence on measures count ( $$n$$ ) …