Statistical inference for Bures--Wasserstein barycenters
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2788 | |
dc.contributor.author | Kroshnin, Alexey | |
dc.contributor.author | Spokoiny, Vladimir | |
dc.contributor.author | Suvorikova, Alexandra | |
dc.date.accessioned | 2022-06-30T13:24:02Z | |
dc.date.available | 2022-06-30T13:24:02Z | |
dc.date.issued | 2020 | |
dc.description.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. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9438 | |
dc.identifier.uri | https://doi.org/10.34657/8476 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2788 | |
dc.relation.hasversion | https://doi.org/10.1214/20-AAP1618 | |
dc.relation.issn | 2198-5855 | |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | |
dc.subject.other | Bures-Wasserstein barycenters | eng |
dc.subject.other | central limit theorem | eng |
dc.subject.other | optimal transport | eng |
dc.title | Statistical inference for Bures--Wasserstein barycenters | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 37 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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