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.

翻译：Bures-Wasserstein barycenter是分析图表、图像等复杂数据的一个流行和有希望的工具。 在许多应用中,输入数据是随机的,分布不明,不确定性的量化成为一个关键问题。 本文提供了一种基于倍增效应陷阱的方法,以量化经验对应方对准真正的Bures-Wasserstein baycenter $ $ $ 的误差。 主要结果显示,根据数据生成分布的一般假设,靴带的有效性为$ P$ 美元,并规定了亚爆炸值 $ P$ 的近似率。 该方法的性能通过加权随机区块模型产生的合成数据加以说明。