Multiplier bootstrap for Bures-Wasserstein barycenters

11/24/2021
by   Alexey Kroshnin, et al.
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Bures-Wasserstein barycenter is a popular and promising tool in analysis of complex data like graphs, images etc. In many applications the input data are random with an unknown distribution, and uncertainty quantification becomes a crucial issue. This paper offers an approach based on multiplier bootstrap to quantify the error of approximating the true Bures–Wasserstein barycenter Q_* by its empirical counterpart Q_n. The main results state the bootstrap validity under general assumptions on the data generating distribution P and specifies the approximation rates for the case of sub-exponential P. The performance of the method is illustrated on synthetic data generated from the weighted stochastic block model.

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