Oracle Inequalities for Local and Global Empirical Risk Minimizers

DOI10.1007/978-3-319-73074-5_7zbMath1443.62148OpenAlexW2968578771MaRDI QIDQ3296182

Sara van de Geer, Andreas Elsener

Publication date: 7 July 2020

Published in: Applied and Numerical Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-73074-5_7

zbMATH Keywords

classificationoracle inequalityempirical risk minimizer

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Classification and discrimination; cluster analysis (statistical aspects) (62H30) Inequalities; stochastic orderings (60E15) Order statistics; empirical distribution functions (62G30)

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Cites Work

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• Statistics for high-dimensional data. Methods, theory and applications.
• Exponential screening and optimal rates of sparse estimation
• Oracle inequalities in empirical risk minimization and sparse recovery problems. École d'Été de Probabilités de Saint-Flour XXXVIII-2008.
• Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion
• Support recovery without incoherence: a case for nonconvex regularization
• High-dimensional regression with noisy and missing data: provable guarantees with nonconvexity
• Robust low-rank matrix estimation
• The landscape of empirical risk for nonconvex losses
• Statistical consistency and asymptotic normality for high-dimensional robust \(M\)-estimators
• Simultaneous analysis of Lasso and Dantzig selector
• Sparsity oracle inequalities for the Lasso
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• Optimization with Sparsity-Inducing Penalties
• Sharp Oracle Inequalities for Stationary Points of Nonconvex Penalized M-Estimators
• Sharp Oracle Inequalities for Square Root Regularization
• On Consistency and Sparsity for Principal Components Analysis in High Dimensions
• Book Reviews
• Weakly decomposable regularization penalties and structured sparsity
• Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima