Statistical inference for Bures-wasserstein barycenters

Alexey Kroshnin, Vladimir Spokoiny, Alexandra Suvorikova

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

In this work we introduce the concept of Bures-Wasserstein barycenter Q, that is essentially a Fréchet mean of some distribution P supported on a subspace of positive semi-definite d-dimensional Hermitian operators H+(d). We allow a barycenter to be constrained to some affine subspace of H+(d), and we provide conditions ensuring its existence and uniqueness. We also investigate convergence and concentration properties of an empirical counterpart of Q in both Frobenius norm and Bures-Wasserstein distance, and explain, how the obtained results are connected to optimal transportation theory and can be applied to statistical inference in quantum mechanics.

Original languageEnglish
Pages (from-to)1264-1298
Number of pages35
JournalAnnals of Applied Probability
Volume31
Issue number3
DOIs
Publication statusPublished - Jun 2021
Externally publishedYes

Keywords

  • Bures-Wasserstein barycenter
  • Central limit theorem
  • Concentration
  • Hermitian operators
  • Wasserstein barycenter

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