Abstract
A selection of probability inequalities from the literature for sums of mean zero matrices is presented. The chapter starts out with recalling Hoeffding’s inequality and Bernstein’s inequality. Then symmetric matrices and rectangular matrices are considered (the latter mostly in Sects. 9.3 and 9.4). The paper Tropp (2012) serves as main reference and in Sect. 9.4 result from Lounici (2011). See also Tropp (2015) for further results.
Keywords
- Probability Inequalities
- Hoeffding
- Rectangular Matrices
- Symmetric Matrices
- Mean Zero
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V. Koltchinskii, K. Lounici, A. Tsybakov, Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion. Ann. Stat. 39, 2302–2329 (2011)
R.I. Oliveira, Sums of random Hermitian matrices and an inequality by Rudelson. Electron. Commun. Probab. 15, 26 (2010)
J. Tropp, User-friendly tail bounds for sums of random matrices. Found. Comput. Math. 12, 389–434 (2012)
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© 2016 Springer International Publishing Switzerland
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van de Geer, S. (2016). Probability Inequalities for Matrices. In: Estimation and Testing Under Sparsity. Lecture Notes in Mathematics(), vol 2159. Springer, Cham. https://doi.org/10.1007/978-3-319-32774-7_9
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DOI: https://doi.org/10.1007/978-3-319-32774-7_9
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