Fetching the paper…
Reading the bibliography…
We obtain estimation error rates and sharp oracle inequalities for regularization procedures of the form \begin{equation*} \hat f \in argmin_{f\in F}\left(\frac{1}{N}\sum_{i=1}^N\ell(f(X_i), Y_i)+\lambda \|f\|\right) \end{equation*} when $\|\cdot\|$ is any norm, $F$ is a convex class of functions and $\ell$ is a Lipschitz loss function satisfying a Bernstein condition over $F$.
Robust estimation of a location parameter
Peter J. Huber · 1964
Earlier work this paper cites.
Real analysis and probability
R. M. Dudley · 1989
Earlier work this paper cites.
Probability in Banach spaces
Michel Ledoux and Michel Talagrand · 1991
Earlier work this paper cites.
Theory of Orlicz spaces
M. M. Rao and Z. D. Ren · 1991
Earlier work this paper cites.
Statistical learning theory
Vladimir N. Vapnik · 1998
Earlier work this paper cites.
Polychotomous logistic regression via the Lasso
Carmen Mak · 1999
Earlier work this paper cites.
Smooth discrimination analysis
E. Mammen and A. Tsybakov · 1999
Earlier work this paper cites.
Applications of empirical process theory
Sara A. van de Geer · 2000
Earlier work this paper cites.
On the mathematical foundations of learning
Felipe Cucker and Steve Smale · 2002
Earlier work this paper cites.
Empirical margin distributions and bounding the generalization error of combined classifiers
V. Koltchinskii and D. Panchenko · 2002
Earlier work this paper cites.
Improving the sample complexity using global data
Shahar Mendelson · 2002
Earlier work this paper cites.
Applications of Orlicz spaces
M. M. Rao and Z. D. Ren · 2002
Earlier work this paper cites.
Large margin classifiers: Convex loss, low noise, and convergence rates
Peter L Bartlett, Michael I Jordan, and Jon D McAuliffe · 2003
Earlier work this paper cites.
Statistical learning theory and stochastic optimization: Ecole d’Eté de Probabilités de Saint-Flour, XXXI-2001
Olivier Catoni · 2004
Earlier work this paper cites.
On the performance of kernel classes
Shahar Mendelson · 2004
Earlier work this paper cites.
Maximum-margin matrix factorization
Nathan Srebro, Jason Rennie, and Tommi S Jaakkola · 2004
Earlier work this paper cites.
Optimal aggregation of classifiers in statistical learning
Alexandre B. Tsybakov · 2004
Earlier work this paper cites.
Statistical behavior and consistency of classification methods based on convex risk minimization
Tong Zhang · 2004
Earlier work this paper cites.
A probabilistic approach to the geometry of the
Franck Barthe, Olivier Guédon, Shahar Mendelson, and Assaf Naor · 2005
Earlier work this paper cites.
Local Rademacher complexities
Peter L. Bartlett, Olivier Bousquet, and Shahar Mendelson · 2005
Earlier work this paper cites.
Theory of classification: a survey of some recent advances
Stéphane Boucheron, Olivier Bousquet, and Gábor Lugosi · 2005
Earlier work this paper cites.
The generic chaining
Michel Talagrand · 2005
Earlier work this paper cites.
Convexity, classification, and risk bounds
Peter L Bartlett, Michael I Jordan, and Jon D McAuliffe · 2006
Cited alongside, same era.
Empirical minimization
Peter L. Bartlett and Shahar Mendelson · 2006
Cited alongside, same era.
Local Rademacher complexities and oracle inequalities in risk minimization
Vladimir Koltchinskii · 2006
Cited alongside, same era.
Fast learning rates for plug-in classifiers
Jean-Yves Audibert and Alexandre B. Tsybakov · 2007
Cited alongside, same era.
Pac-bayesian supervised classification: the thermodynamics of statistical learning
Olivier Catoni · 2007
Cited alongside, same era.
Optimal rates of aggregation in classification under low noise assumption
Guillaume Lecué · 2007
Cited alongside, same era.
Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
Vladimir Koltchinskii, Karim Lounici, and Alexandre B. Tsybakov · 2011
Later among the works it cites.
Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
Vladimir Koltchinskii, Karim Lounici, Alexandre B Tsybakov, et al · 2011
Later among the works it cites.
Interplay between concentration, complexity and geometry in learning theory with applications to high dimensional data analysis
Guillaume Lecué · 2011
Later among the works it cites.
Estimation of high-dimensional low-rank matrices
Angelika Rohde and Alexandre B Tsybakov · 2011
Later among the works it cites.
Interactions between compressed sensing random matrices and high dimensional geometry
Djalil Chafaï, Olivier Guédon, Guillaume Lecué, and Alain Pajor · 2012
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Oracle inequalities in empirical risk minimization and sparse recovery problems
Vladimir Koltchinskii · 2008
Cited alongside, same era.
The group Lasso for logistic regression
Lukas Meier, Sara van de Geer, and Peter Bühlmann · 2008
Cited alongside, same era.
Obtaining fast error rates in nonconvex situations
Shahar Mendelson · 2008
Cited alongside, same era.
Support vector machines
Ingo Steinwart and Andreas Christmann · 2008
Cited alongside, same era.
Efficient methods for estimating constrained parameters with applications to regularized (lasso) logistic regression
Guo-Liang Tian, Man-Lai Tang, Hong-Bin Fang, and Ming Tan · 2008
Cited alongside, same era.
High-dimensional generalized linear models and the lasso
Sara A Van de Geer · 2008
Cited alongside, same era.
Venkat Chandrasekaran, Benjamin Recht, Pablo A. Parrilo, and Alan S. Willsky · 2012
Later among the works it cites.
General nonexact oracle inequalities for classes with a subexponential envelope
Guillaume Lecué and Shahar Mendelson · 2012
Later among the works it cites.
Learning subgaussian classes: Upper and minimax bounds
Guillaume Lecué and Shahar Mendelson · 2013
Later among the works it cites.
EMLasso: logistic lasso with missing data
N. Sabbe, O. Thas, and J.-P. Ottoy · 2013
Later among the works it cites.
1-bit matrix completion
Mark A Davenport, Yaniv Plan, Ewout van den Berg, and Mary Wootters · 2014
Later among the works it cites.
Nuclear norm minimization via active subspace selection
Cho-Jui Hsieh and Peder A Olsen · 2014
Later among the works it cites.
Noisy low-rank matrix completion with general sampling distribution
O. Klopp · 2014
Later among the works it cites.
Probabilistic low-rank matrix completion on finite alphabets
Jean Lafond, Olga Klopp, Eric Moulines, and Joseph Salmon · 2014
Later among the works it cites.
SLOPE—adaptive variable selection via convex optimization
Małgorzata Bogdan, Ewout van den Berg, Chiara Sabatti, Weijie Su, and Emmanuel J. Candès · 2015
Later among the works it cites.
Regularization and the small-ball method I: sparse recovery
Guillaume Lecué and Shahar Mendelson · 2015
Later among the works it cites.
Regularization and the small-ball method II: complexity dependent error rates
Guillaume Lecué and Shahar Mendelson · 2015
Later among the works it cites.
A bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution
T. T. Mai and P. Alquier · 2015
Later among the works it cites.
Estimation and testing under sparsity
Sara van de Geer · 2015
Later among the works it cites.
On the properties of variational approximations of gibbs posteriors
Pierre Alquier, James Ridgway, and Nicolas Chopin · 2016
Later among the works it cites.
1-bit Matrix Completion: PAC-Bayesian Analysis of a Variational Approximation
V. Cottet and P. Alquier · 2016
Later among the works it cites.
Robust low-rank matrix estimation
Andreas Elsener and Sara van de Geer · 2016
Later among the works it cites.
SLOPE is adaptive to unknown sparsity and asymptotically minimax
Weijie Su and Emmanuel Candès · 2016
Later among the works it cites.