Electronic Communications in Probability

Tail inequalities for sums of random matrices that depend on the intrinsic dimension

Daniel Hsu, Sham Kakade, and Tong Zhang

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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.

Article information

Source
Electron. Commun. Probab. Volume 17 (2012), paper no. 14, 13 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465263147

Digital Object Identifier
doi:10.1214/ECP.v17-1869

Mathematical Reviews number (MathSciNet)
MR2900355

Zentralblatt MATH identifier
1243.60007

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Hsu, Daniel; Kakade, Sham; Zhang, Tong. Tail inequalities for sums of random matrices that depend on the intrinsic dimension. Electron. Commun. Probab. 17 (2012), paper no. 14, 13 pp. doi:10.1214/ECP.v17-1869. https://projecteuclid.org/euclid.ecp/1465263147


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