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2012 Tail inequalities for sums of random matrices that depend on the intrinsic dimension
Daniel Hsu, Sham Kakade, Tong Zhang
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Electron. Commun. Probab. 17: 1-13 (2012). DOI: 10.1214/ECP.v17-1869

Abstract

This work provides exponential tail inequalities for sums of random matrices that depend only on intrinsic dimensions rather than explicit matrix dimensions. These tail inequalities are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit matrix dimensions replaced by a trace quantity that can be small even when the explicit dimensions are large or infinite. Some applications to covariance estimation and approximate matrix multiplication are given to illustrate the utility of the new bounds.

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Daniel Hsu. Sham Kakade. Tong Zhang. "Tail inequalities for sums of random matrices that depend on the intrinsic dimension." Electron. Commun. Probab. 17 1 - 13, 2012. https://doi.org/10.1214/ECP.v17-1869

Information

Accepted: 12 March 2012; Published: 2012
First available in Project Euclid: 7 June 2016

zbMATH: 1243.60007
MathSciNet: MR2900355
Digital Object Identifier: 10.1214/ECP.v17-1869

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