Gaussian approximation for penalized Wasserstein barycenters

Nazar Buzun

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arXiv · 1904.00891

Gaussian approximation for penalized Wasserstein barycenters

Nazar Buzun

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Abstract

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 by distribution. The convergence rate has been derived in finite-sample case with explicit dependence on measures count ($n$) and the dimension of parameters ($p$).

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Nazar Buzun. 2019-04-01. Gaussian approximation for penalized Wasserstein barycenters. https://arxiv.org/abs/1904.00891

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