Non-injectivity of Bures--Wasserstein barycentres in infinite dimensions

2023/11/15 by Zemel, Yoav
#FOS: Mathematics #Functional Analysis (math.FA) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2311.09385

Abstract

We construct a counterexample to the injectivity conjecture of Masarotto et al (2018). Namely, we construct a class of examples of injective covariance operators on an infinite-dimensional separable Hilbert space for which the Bures--Wasserstein barycentre is highly non injective -- it has a kernel of infinite dimension.

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