Rejoinder: Local Rademacher complexities and oracle inequalities in risk minimization

By Vladimir Koltchinskii. 2006

192 citations recorded by the source corpus.

Rejoinder: 2004 IMS Medallion Lecture: Local Rademacher complexities and oracle inequalities in risk minimization [arXiv:0708.0083]

Subfields: Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

Deep Neural Networks for Estimation and Inference: Application to Causal Effects and Other Semiparametric Estimands (2018, background): “Our analysis of deep nets instead employs localization methods (Koltchinskii and Panchenko, 2000; Bartlett, Bousquet, Mendelson, et al., 2005; Koltchinskii, 2006; Liang, Rakhlin, and Sridharan, 2015), along with the recent approximation work of Yarotsky (2017, 2018) and complexity results of Bartlet”
A high-dimensional Wilks phenomenon (2011, background): “A different style of presentation and derivation can be found in (Koltchinskii 2006).”
Random Design Analysis of Ridge Regression (2011, unknown): “Finally, although the focus of our present work is on understanding the ordinary least squares and ridge estimators, it should also be mentioned that a number of other estimators have been considered in the literature with nonasymptotic prediction error bounds [3,13,14].”
Oracle inequalities for computationally adaptive model selection (2012, background): “Under suitable assumptions, complexity regularization can also achieve fast rates for model selection [8, 17].”
Relative deviation learning bounds and generalization with unbounded loss functions (2013, background): “…1998), Rademacher complexity (Koltchinskii and Panchenko, 2000; Bartlett et al., 2002a; Koltchinskii and Panchenko, 2002; Bartlett and Mendelson, 2002) or local Rademacher complexity bounds (Koltchinskii, 2006; Bartlett et al., 2002b), as well as most other bounds based on other complexity terms.”
Direct importance estimation for covariate shift adaptation (2008, methodology): “Following the line of Koltchinskii (2006), for ε = ε1 + · · ·+ εm, we have (ψ1 + · · ·+ ψm)(ε) ≤ ψ 1 (ε1) ∨ · · · ∨ ψ m(εm).”
Nonparametric regression using deep neural networks with ReLU activation function (2017, background): “r with (7.16) the upper bounds in (3.3) and (3.4) follow for any constant C. This completes the proof. 7.4 Proof of Theorem 2 Several oracle inequalities for the least-squares estimator are know, cf. [14, 27, 11, 15, 32]. The common assumption of bounded response variables is, however, violated in t”
Fast learning rates for plug-in classifiers (2005, background): “A standard complexity assumption on the decision set (CAD) is the following.”
Early stopping for non-parametric regression: An optimal data-dependent stopping rule (2011, methodology): “1 Stopping Rules and General Error Bounds Our stopping rule involves the use of a model complexity measure, familiar from past work on uniform laws over kernel classes (Bartlett et al., 2005; Koltchinskii, 2006; Mendelson, 2002), known as the local empirical Rademacher complexity.”
Singularity, misspecification and the convergence rate of EM (2018, background): “We note that similar ideas of localizing an empirical process plays a crucial role in obtaining sharp bounds on the error of M -estimation procedures [26, 2, 16].”