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We obtain risk bounds for Empirical Risk Minimizers (ERM) and minmax Median-Of-Means (MOM) estimators based on loss functions that are both Lipschitz and convex.
Problem complexity and method efficiency in optimization
A. S. Nemirovsky and D. B. Yudin · 1983
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Stabilité et instabilité du risque minimax pour des variables indépendantes équidistribuées
Lucien Birgé · 1984
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Random generation of combinatorial structures from a uniform distribution
Mark R. Jerrum, Leslie G. Valiant, and Vijay V. Vazirani · 1986
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The Nature of Statistical Learning Theory
Vladimir Vapnik · 1995
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The space complexity of approximating the frequency moments
Noga Alon, Yossi Matias, and Mario Szegedy · 1996
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Statistical learning theory
Vladimir Vapnik · 1998
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Smooth discrimination analysis
Enno Mammen and Alexandre B. Tsybakov · 1999
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The concentration of measure phenomenon
Michel Ledoux · 2001
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Optimal aggregation of classifiers in statistical learning
Alexandre B. Tsybakov · 2004
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Local Rademacher complexities
Peter L. Bartlett, Olivier Bousquet, and Shahar Mendelson · 2005
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Local rademacher complexities
Peter L Bartlett, Olivier Bousquet, Shahar Mendelson, et al · 2005
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Theory of classification: a survey of some recent advances
Stéphane Boucheron, Olivier Bousquet, and Gábor Lugosi · 2005
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Empirical minimization
Peter L. Bartlett and Shahar Mendelson · 2006
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Local Rademacher complexities and oracle inequalities in risk minimization
Vladimir Koltchinskii · 2006
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Reconstruction and subgaussian operators in asymptotic geometric analysis
Shahar Mendelson, Alain Pajor, and Nicole Tomczak-Jaegermann · 2007
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Oracle inequalities in empirical risk minimization and sparse recovery problems
Vladimir Koltchinskii · 2008
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Robust linear least squares regression
Jean-Yves Audibert and Olivier Catoni · 2011
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Convex optimization with sparsity-inducing norms
Francis Bach, Rodolphe Jenatton, Julien Mairal, Guillaume Obozinski, et al · 2011
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Robust statistics
Peter J Huber and E. Ronchetti · 2011
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Empirical and rademacher processes
Vladimir Koltchinskii · 2011
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Scikit-learn: Machine learning in Python
F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay · 2011
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Sub-gaussian mean estimators
Luc Devroye, Matthieu Lerasle, Gabor Lugosi, Roberto I Oliveira, et al · 2016
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Robust low-rank matrix estimation
Andreas Elsener and Sara van de Geer · 2016
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Performance of empirical risk minimization in linear aggregation
Guillaume Lecué and Shahar Mendelson · 2016
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Risk minimization by median-of-means tournaments
Gabor Lugosi and Shahar Mendelson · 2016
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P. Alquier, V. Cottet, and G. Lecué · 2017
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A new method for estimation and model selection:
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Challenging the empirical mean and empirical variance: a deviation study
Olivier Catoni · 2012
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Concentration inequalities
Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
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Probability in Banach Spaces: isoperimetry and processes
Michel Ledoux and Michel Talagrand · 2013
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Learning without concentration
Shahar Mendelson · 2014
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Upper and lower bounds for stochastic processes
Michel Talagrand · 2014
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Convex optimization: Algorithms and complexity
Sébastien Bubeck · 2015
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Y. Baraud, L. Birgé, and M. Sart · 2017
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Convergence rates of least squares regression estimators with heavy-tailed errors
Qiyang Han and Jon A. Wellner · 2017
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Learning from mom’s principles: Le cam’s approach
G. Lecué and M. Lerasle · 2017
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Robust machine learning by median-of-means: theory and practice
G. Lecué and M. Lerasle · 2017
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Regularization, sparse recovery, and median-of-means tournaments
Gabor Lugosi and Shahar Mendelson · 2017
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Sub-gaussian estimators of the mean of a random vector
Gabor Lugosi and Shahar Mendelson · 2017
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On multiplier processes under weak moment assumptions
Shahar Mendelson · 2017
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Robust classification via mom minimization
G. Lecué, M. Lerasle, and T. Mathieu · 2018
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On optimality of empirical risk minimization in linear aggregation
Adrien Saumard · 2018
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A new perspective on robust m-estimation: Finite sample theory and applications to dependence-adjusted multiple testing
W.-X. Zhou, K. Bose, J. Fan, and H. Liu · 2018
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