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We study prediction and estimation problems using empirical risk minimization, relative to a general convex loss function.
Some limit theorems for empirical processes
Evarist Giné and Joel Zinn · 1984
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Asymptotic theory of finite-dimensional normed spaces
Vitali D. Milman and Gideon Schechtman · 1986
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Subspaces of small codimension of finite-dimensional Banach spaces
Alain Pajor and Nicole Tomczak-Jaegermann · 1986
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The volume of convex bodies and Banach space geometry
Gilles Pisier · 1989
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Probability in Banach spaces
Michel Ledoux and Michel Talagrand · 1991
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Rates of convergence for minimum contrast estimators
Lucien Birgé and Pascal Massart · 1993
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A probabilistic theory of pattern recognition
Luc Devroye, László Györfi, and Gábor Lugosi · 1996
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The importance of convexity in learning with squared loss
W. S. Lee, P. L. Bartlett, and R. C. Williamson · 1996
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Weak convergence and empirical processes
Aad W. van der Vaart and Jon A. Wellner · 1996
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Decoupling
Víctor H. de la Peña and Evarist Giné · 1999
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Uniform central limit theorems
R. M. Dudley · 1999
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The Concnetration of Measure Phenomenon
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Pascal Massart · 2003
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Introduction to nonparametric estimation
Alexandre B. Tsybakov · 2004
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Local Rademacher complexities
Peter L. Bartlett, Olivier Bousquet, and Shahar Mendelson · 2005
Obtaining fast error rates in nonconvex situations
Shahar Mendelson · 2008
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Statistics for high-dimensional data
Peter Bühlmann and Sara van de Geer · 2011
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Concentration Inequalities: A Nonasymptotic Theory of Independence
Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
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Learning subgaussian classes: Upper and minimax bounds
Guillaume Lecué and Shahar Mendelson · 2013
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Learning without concentration
Shahar Mendelson · 2013
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On the geometry of subgaussian coordinate projections
Shahar Mendelson · 2013
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Empirical minimization
Peter L. Bartlett and Shahar Mendelson · 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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A remark on the diameter of random sections of convex bodies
Shahar Mendelson · 2013
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Isomorphic and almost isometric bounds using the small-ball method
Shahar Mendelson · 2014
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Upper and lower bounds for stochastic processes
Michel Talagrand · 2014
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