Local Rademacher complexities and oracle inequalities in risk minimization

By Peter L. Bartlett, Shahar Mendelson. 2006

400 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Numerical Analysis, Statistics and Probability

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Citations in the corpus

GLOBAL UNIFORM RISK BOUNDS FOR WAVELET DECONVOLUTION ESTIMATORS (2011, methodology): “We suggest a new approach to nonparametric confidence bands based on Rademacher symmetrization, in a similar vein as in recent work of Koltchinskii [29].”
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).”
Sharp oracle inequalities for Least Squares estimators in shape restricted regression (2015, methodology): “3 is related to the isomorphic method [2] and the theory of local Rademacher complexities in regression with random design [3, 12].”
Relative deviation learning bounds and generalization with unbounded loss functions (2013, background): “(Vapnik, 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 ”
Oracle inequalities in empirical risk minimization and sparse recovery problems (2011, methodology): “Our approach to this problem has been already outlined in the Introduction and it is closely related to the recent work of Massart [73], Koltchinskii and Panchenko [60], Bartlett, Bousquet and Mendelson [7], Bousquet, Koltchinskii and Panchenko [23], Koltchinskii [59], Bartlett and Mendelson [9].”
Sparsity in penalized empirical risk minimization (2009, methodology): “We will frequently use the symmetrization inequality, contraction inequality and other standard facts about Rademacher processes that can be found in [18,27] and, in the context close to this paper, in [16].”
DEEP NEURAL NETWORKS FOR ESTIMATION AND INFERENCE (2020, positive): “…of our proof is to use a scale sensitive localization theory (Koltchinskii and Panchenko (2000), Bartlett, Bousquet, and Mendelson (2005), Koltchinskii (2006, 2011), Liang, Rakhlin, and Sridharan (2015)) with such scale insensitive measures for deep neural networks for general smooth…”
A No-Free-Lunch Theorem for MultiTask Learning (2020, methodology): “ below. The proof will rely on the following lemma: a uniform Bernstein inequality for independent but non-identically distributed data. Results of this type are well known for i.i.d. data (see e.g., [Kol06]). For completeness, we include a proof of the extension to non-identically distributed data ”
Robust machine learning by median-of-means: Theory and practice (2017, background): “ 2. E(Y i X i;t )2 = E(Y X;t )2, 3. E(Y X;t )2 X;t 2 6 2 mE X;t 2 , 4. q E X;t 2 6 0Ej X;t j. Let us now compute the xed points r Q( Q) and r M( M). The proof essentially follows from Example 1 in [45]. Let JˆIbe such that jJj> N=2. Denote by V ˆRd the smallest linear span containing almost sure”
On the Value of Target Data in Transfer Learning (2020, background): “The first one is a so-called Bernstein Class Condition on noise [26, 27, 28, 29, 30].”
Parametric or nonparametric? A parametricness index for model selection (2011, background): “Publications of work in this direction include [3–6, 10, 13, 15, 22–24, 42, 69], to name a few.”