A Few Notes on Statistical Learning Theory

By Shahar Mendelson. 2002

207 citations recorded by the source corpus.

Subfields: Applied Mathematics, Artificial Intelligence

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Artificial Intelligence

Citations in the corpus

Deep Neural Networks for Estimation and Inference: Application to Causal Effects and Other Semiparametric Estimands (2018, methodology): “Next, we give two properties of the Rademacher complexity (see Mendelson, 2003).”
Kernel methods in machine learning (2007, neutral): “We refer to the works of Bartlett and Mendelson [12], Jordan et al. [80], Koltchinskii [86], Mendelson [98] and Vapnik [141] for details.”
Just Interpolate: Kernel "Ridgeless" Regression Can Generalize (2018, background): “See (Mendelson, 2003, Theorem 2.21, 2.23 and their corollaries).”
Learning with Square Loss: Localization through Offset Rademacher Complexity (2015, methodology): “In a nutshell, it extends the classical probabilistic symmetrization technique [7, 13] to the non-zero-mean offset process under the investigation.”
Training generative neural networks via Maximum Mean Discrepancy optimization (2015, methodology): “Theorem 2 (McDiarmids Inequality [8]) .”
A study in Rashomon curves and volumes: A new perspective on generalization and model simplicity in machine learning (2019, methodology): “The use of approximating sets, as used extensively in this paper, is used throughout the literature on learning theory [28, 31, 38, 33].”
Nonparametric Quantile Estimation (2006, methodology): “In this case it follows from Mendelson (2003) that Rm(F ) ≤ 2C √m.”
Generalized Non-Parametric Deconvolution with an Application to Earnings Dynamics (2010, methodology): “Lastly, both (12)Notice that model (28) implies that Var (∆syit) − Var (∆yit) = (s− 1)σ2ε.”
The Tradeoffs of Large Scale Learning (2007, background): “Combining this result with standard bounds on the complexity of classes of linear functions (e.g., Bousquet, 2002) yields the following result: See also (Mendelson, 2003; Bartlett and Mendelson, 2006) for more bounds taking into account the optimization accuracy.”
Provable and Efficient Continual Representation Learning (2022, methodology): “To quantify the complexities of the search spaces Φ new , H , we introduce metric dimension (Mendelson (2003)), which is a generalization of the VC-dimension (Vapnik and Chervonenkis (2015)).”
Correcting Sample Selection Bias by Unlabeled Data (2006, result): “Proof The proof strategy is almost identical to the one of Lemma 4 an d [10].”
Rademacher Chaos Complexities for Learning the Kernel Problem (2010, unknown): “gif" alt-version="no" mimetype="image" xlink:type="simple"> Then we use the following Dudley's entropy bound (Mendelson, 2002 , 2003 ).”
Sequential complexities and uniform martingale laws of large numbers (2015, methodology): “In empirical process theory, such structural results are obtained through properties of Rademacher averages [18, 7].”
Generalization Bounds for Domain Adaptation (2012, methodology): “In the learning process of domain adaptation with multiple sources, we are mainly interested in the following two types of quantities: • E(T )(ℓ ◦ gw)−E(S)w (ℓ ◦ gw), which corresponds to the estimation of the expected risk in the target domain Z(T ) from the empirical quantity that is the weighted…”
Consistency of spectral clustering (2008, background): “As we have C ( X ) ⊂ L 2 ( P ) by the compactness of X , the same holds for the eigenvalues of U as an operator on C ( ).”