Multiplier bootstrap for Bures-Wasserstein barycenters

Alexey Kroshnin, Alexandra Suvorikova, Vladimir Spokoiny

Publication date: 24 November 2021

Abstract: 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.

Has companion code repository: https://github.com/asuvor/bw_paper

Mathematics Subject Classification ID

Bootstrap, jackknife and other resampling methods (62F40)

This page was built for publication: Multiplier bootstrap for Bures-Wasserstein barycenters

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6383879)