On singular values of matrices with independent rows

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Excess risk bounds for multitask learning with trace norm regularization (2012, methodology): “(cid:22) Summing this relation over k and passing to the largest eigenvalue yields Now we combine Markov’s inequality with Theorem 6 (i) and the last inequality to obtain (cid:0) (cid:1) (cid:0) (cid:1) The next result and its proof are essentially due to Oliveira ([24], Lemma 1, but see also [23].”
On Learning with Integral Operators (2010, background): “These investigations were continued in Mendelson and Pajor (2005) and Mendelson and Pajor (2006), where it was shown that, under the assumption that the kernel is of positive type, the problem of eigenvalue convergence reduces to the study of how the random operator 1 n ∑ n i=1 X i ⊗ X i deviates…”
Sums of random Hermitian matrices and an inequality by Rudelson (2010, background): “While similar results have appeared in other papers [10, 12, 16], our proof is simpler and gives explicit (albeit quite large) constants.”
Quantitative estimates of the convergence of the empirical covariance matrix in log-concave ensembles (2009, background): “1) with overwhelming probability was given in [18].”
Compressive Sensing with structured random matrices (2012, unknown): “Similar techniques were used in [92].”