LSV-based tail inequalities for sums of random matrices

Zhang, C; Du, L; Tao, D

LSV-based tail inequalities for sums of random matrices

Zhang, C Du, L Tao, D

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Publication Type:: Journal Article
Citation:: Neural Computation, 2017, 29 (1), pp. 247 - 262
Issue Date:: 2017-01-01

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Field	Value	Language
dc.contributor.author	Zhang, C	en_US
dc.contributor.author	Du, L	en_US
dc.contributor.author	Tao, D https://orcid.org/0000-0001-7225-5449	en_US
dc.date.issued	2017-01-01	en_US
dc.identifier.citation	Neural Computation, 2017, 29 (1), pp. 247 - 262	en_US
dc.identifier.issn	0899-7667	en_US
dc.identifier.uri	http://hdl.handle.net/10453/123844
dc.description.abstract	© 2016 Massachusetts Institute of Technology. The techniques of random matrices have played an important role in many machine learning models. In this letter, we present a new method to study the tail inequalities for sums of random matrices. Different from other work (Ahlswede & Winter, 2002; Tropp, 2012; Hsu, Kakade, & Zhang, 2012), our tail results are based on the largest singular value (LSV) and independent of the matrix dimension. Since the LSV operation and the expectation are noncommutative, we introduce a diagonalization method to convert the LSV operation into the trace operation of an infinitely dimensional diagonal matrix. In thisway,we obtain another version of Laplace-transform bounds and then achieve the LSV-based tail inequalities for sums of random matrices.	en_US
dc.relation	http://purl.org/au-research/grants/arc/FT130101457
dc.relation	http://purl.org/au-research/grants/arc/DP140102164
dc.relation.ispartof	Neural Computation	en_US
dc.relation.isbasedon	10.1162/NECO_a_00901	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	LSV-based tail inequalities for sums of random matrices	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	29	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	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
utslib.copyright.status	open_access
pubs.issue	1	en_US
pubs.publication-status	Published	en_US
pubs.volume	29	en_US

Abstract:

© 2016 Massachusetts Institute of Technology. The techniques of random matrices have played an important role in many machine learning models. In this letter, we present a new method to study the tail inequalities for sums of random matrices. Different from other work (Ahlswede & Winter, 2002; Tropp, 2012; Hsu, Kakade, & Zhang, 2012), our tail results are based on the largest singular value (LSV) and independent of the matrix dimension. Since the LSV operation and the expectation are noncommutative, we introduce a diagonalization method to convert the LSV operation into the trace operation of an infinitely dimensional diagonal matrix. In thisway,we obtain another version of Laplace-transform bounds and then achieve the LSV-based tail inequalities for sums of random matrices.

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http://hdl.handle.net/10453/123844