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We prove a new and general concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise.
Risk bounds for model selection via penalization
A. Barron, L. Birgé, and P. Massart · 1999
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A Bennett concentration inequality and its application to suprema of empirical processes
O. Bousquet · 2002
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Concentration inequalities and model selection
P. Massart · 2003
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Concentration around the mean for maxima of empirical processes
T. Klein and E. Rio · 2005
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Minimal penalties for Gaussian model selection
L. Birgé and P. Massart · 2007
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V V -fold cross-validation improved: V V -fold penalization, February 2008
S. Arlot · 2008
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Oracle inequalities in empirical risk minimization and sparse recovery problems
V. Koltchinskii · 2008
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Data-driven calibration of linear estimators with minimal penalties
S. Arlot and F. Bach · 2009
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Data-driven calibration of penalties for least-squares regression
S. Arlot and P. Massart · 2009
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Simultaneous analysis of lasso and Dantzig selector
P. J. Bickel, Y. Ritov, and A. B. Tsybakov · 2009
Cited alongside, same era.
Regular Contrast Estimation and the Slope Heuristics
A. Saumard · 2010
Cited alongside, same era.
A high-dimensional Wilks phenomenon
S. Boucheron and P. Massart · 2011
Cited alongside, same era.
Interplay between concentration, complexity and geometry in learning theory with applications to high dimensional data analysis
G. Lecué · 2011
Cited alongside, same era.
Optimal model selection for density estimation of stationary data under various mixing conditions
M. Lerasle · 2011
Cited alongside, same era.
Slope heuristics: overview and implementation
J.-P. Baudry, C. Maugis, and B. Michel · 2012
Cited alongside, same era.
Choice of V V for V V -fold cross-validation in least-squares density estimation
S. Arlot and M. Lerasle · 2015
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Concentration behavior of the penalized least squares estimator
A. Muro and S. van de Geer · 2015
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Towards the study of least squares estimators with convex penalty
P. C. Bellec, G. Lecué, and A. B. Tsybakov · 2017
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Bounds on the prediction error of penalized least squares estimators with convex penalty
P. C. Bellec and A. B. Tsybakov · 2017
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Slope heuristics and v v -fold model selection in heteroscedastic regression using strongly localized bases
F. Navarro and A. Saumard · 2017
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Optimal upper and lower bounds for the true and empirical excess risks in heteroscedastic least-squares regression
A. Saumard · 2012
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Optimal cross-validation in density estimation with the l 2 l^{2} -loss
A. Celisse · 2014
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A new perspective on least squares under convex constraint
S. Chatterjee · 2014
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On concentration for (regularized) empirical risk minimization
S. van de Geer and M. J. Wainwright · 2017
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Slope meets lasso: improved oracle bounds and optimality
P. C. Bellec, G. Lecué, and A. B. Tsybakov · 2018
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On optimality of empirical risk minimization in linear aggregation
Adrien Saumard · 2018
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