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Second-Order Matrix Concentration Inequalities

Tropp, Joel A. (2015) Second-Order Matrix Concentration Inequalities. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20180831-112133957

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Abstract

Matrix concentration inequalities give bounds for the spectral-norm deviation of a random matrix from its expected value. These results have a weak dimensional dependence that is sometimes, but not always, necessary. This paper identifies one of the sources of the dimensional term and exploits this insight to develop sharper matrix concentration inequalities. In particular, this analysis delivers two refinements of the matrix Khintchine inequality that use information beyond the matrix variance to reduce or eliminate the dimensional dependence.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1504.05919arXivDiscussion Paper
ORCID:
AuthorORCID
Tropp, Joel A.0000-0003-1024-1791
Additional Information:Date: 13 March 2015. Revised 21 April 2015 and 3 August 2016. Afonso Bandeira is responsible for the argument in Section 4.3, and Ramon van Handel has offered critical comments. Parts of this research were completed at Mathematisches Forschungsinstitut Oberwolfach (MFO) and at Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro. The author gratefully acknowledges support from ONR award N00014-11-1002, a Sloan Research Fellowship, and the Gordon & Betty Moore Foundation.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-11-1002
Alfred P. Sloan FoundationUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Subject Keywords:Concentration inequality, moment inequality, random matrix
Classification Code:2010 Mathematics Subject Classification. Primary: 60B20. Secondary: 60F10, 60G50, 60G42
Record Number:CaltechAUTHORS:20180831-112133957
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180831-112133957
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:89337
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:04 Sep 2018 14:34
Last Modified:04 Sep 2018 14:34

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