Characterizations of matrix and operator-valued Φ-entropies, and operator Efron-Stein inequalities

Cheng, HC; Hsieh, MH

Characterizations of matrix and operator-valued Φ-entropies, and operator Efron-Stein inequalities

Cheng, HC

Hsieh, MH

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Publication Type:: Journal Article
Citation:: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2016, 472 (2187)
Issue Date:: 2016-03-01

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Field	Value	Language
dc.contributor.author	Cheng, HC https://orcid.org/0000-0003-4499-4679	en_US
dc.contributor.author	Hsieh, MH https://orcid.org/0000-0002-3396-8427	en_US
dc.date.issued	2016-03-01	en_US
dc.identifier.citation	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2016, 472 (2187)	en_US
dc.identifier.issn	1364-5021	en_US
dc.identifier.uri	http://hdl.handle.net/10453/43727
dc.description.abstract	© 2016 The Author(s). We derive new characterizations of the matrix Φ-entropy functionals introduced in Chen & Tropp (Chen, Tropp 2014 Electron. J. Prob. 19, 1-30. (doi:10.1214/ejp.v19-2964)). These characterizations help us to better understand the properties of matrix Φ-entropies, and are a powerful tool for establishing matrix concentration inequalities for random matrices. Then, we propose an operator-valued generalization of matrix Φ-entropy functionals, and prove the subadditivity under Löwner partial ordering. Our results demonstrate that the subadditivity of operator-valued Φ-entropies is equivalent to the convexity. As an application, we derive the operator Efron-Stein inequality.	en_US
dc.relation	http://purl.org/au-research/grants/arc/FT140100574
dc.relation.ispartof	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences	en_US
dc.relation.isbasedon	10.1098/rspa.2015.0563	en_US
dc.title	Characterizations of matrix and operator-valued Φ-entropies, and operator Efron-Stein inequalities	en_US
dc.type	Journal Article
utslib.citation.volume	2187	en_US
utslib.citation.volume	472	en_US
utslib.for	0105 Mathematical Physics	en_US
utslib.for	080203 Computational Logic and Formal Languages	en_US
utslib.for	0206 Quantum Physics	en_US
utslib.for	01 Mathematical Sciences	en_US
utslib.for	02 Physical Sciences	en_US
utslib.for	09 Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
pubs.organisational-group	/University of Technology Sydney/Students
utslib.copyright.status	open_access
pubs.issue	2187	en_US
pubs.publication-status	Published	en_US
pubs.volume	472	en_US

Abstract:

© 2016 The Author(s). We derive new characterizations of the matrix Φ-entropy functionals introduced in Chen & Tropp (Chen, Tropp 2014 Electron. J. Prob. 19, 1-30. (doi:10.1214/ejp.v19-2964)). These characterizations help us to better understand the properties of matrix Φ-entropies, and are a powerful tool for establishing matrix concentration inequalities for random matrices. Then, we propose an operator-valued generalization of matrix Φ-entropy functionals, and prove the subadditivity under Löwner partial ordering. Our results demonstrate that the subadditivity of operator-valued Φ-entropies is equivalent to the convexity. As an application, we derive the operator Efron-Stein inequality.

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http://hdl.handle.net/10453/43727