On the Performance of Kernel Classes

By Shahar Mendelson. 2003

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Variance-based Regularization with Convex Objectives (2016, methodology): “ 1 2 . (24) As this claim is not central to our development—but does show a slightly diﬀerent localization result based on Gaussian comparison inequalities than available, for example, in Mendelson [34]— we provide its proof in Appendix G.1. Let us use inequality (24). To apply Theorem 3, we must ﬁ”
Optimal Rates for the Regularized Least-Squares Algorithm (2007, background): “Here we show that such information can be used to obtain tighter bounds.”
Active and passive learning of linear separators under log-concave distributions (2012, background): “…process and statistical learning theory literature has taken account of “local complexity” to prove stronger bounds for ERM (van der Vaart and Wellner, 1996; van de Geer, 2000; Bartlett et al., 2005; Long, 2003; Mendelson, 2003; Gin´e and Koltchinskii, 2006; Hanneke, 2007; Hanneke and Yang, 2012).”
Local Rademacher Complexity-based Learning Guarantees for Multi-Task Learning (2016, background): “According to [50], it can be shown that there is a constant c such that if λ 1 t ≥ 1 nR 2 max , then for all r ≥ 1 n it holds , r ) ≥ ∞ j =1 min r, R 2 max T − 2 q λ j 1 , which with some algebra manipulations gives the desired result.”
Tikhonov, Ivanov and Morozov regularization for support vector machine learning (2016, methodology): “…where the value of the input patterns are left unchanged while a random array of labels is assigned to the samples, thus emulating a conventional setup for model selection and error estimation through the Rademacher Complexity (Bartlett and Mendelson 2003; Koltchinskii 2006; Anguita et al. 2012).”
On singular values of matrices with independent rows (2006, background): “[15] and references therein for some theoretical results in this context) but it is not clear how those should be estimated from the given data in the form of the Gram matrix.”
ℓ1-regularized linear regression: persistence and oracle inequalities (2011, unknown): “To control E‖Pn − P‖Gλ we require an additional “peeling” argument, following the same path as in [28].”