Non-injectivity of Bures--Wasserstein barycentres in infinite dimensions
Functional Analysis
2023-11-17 v1 Statistics Theory
Statistics Theory
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.
Keywords
Cite
@article{arxiv.2311.09385,
title = {Non-injectivity of Bures--Wasserstein barycentres in infinite dimensions},
author = {Yoav Zemel},
journal= {arXiv preprint arXiv:2311.09385},
year = {2023}
}