Regularization, sparse recovery, and median-of-means tournaments

DOI10.3150/18-BEJ1046zbMath1467.62131arXiv1701.04112OpenAlexW2963290896MaRDI QIDQ2419670

Shahar Mendelson, Gábor Lugosi

Publication date: 14 June 2019

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.04112

zbMATH Keywords

robust regressionLassomedian-of-means tournamentregularized risk minimizationSlope

Mathematics Subject Classification ID

Ridge regression; shrinkage estimators (Lasso) (62J07) Linear inference, regression (62J99)

Related Items

Unnamed Item, Robust statistical learning with Lipschitz and convex loss functions, Byzantine-robust distributed sparse learning for \(M\)-estimation, Regularization, sparse recovery, and median-of-means tournaments, Unnamed Item, Robust machine learning by median-of-means: theory and practice, Robust classification via MOM minimization, Iteratively reweighted \(\ell_1\)-penalized robust regression, Robust \(k\)-means clustering for distributions with two moments, Convergence rates of least squares regression estimators with heavy-tailed errors, Efficient learning with robust gradient descent, Scale calibration for high-dimensional robust regression, Mean estimation and regression under heavy-tailed distributions: A survey, Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Geometric median and robust estimation in Banach spaces
• Sparse recovery under weak moment assumptions
• Robust linear least squares regression
• Empirical risk minimization for heavy-tailed losses
• On spatially adaptive estimation of nonparametric regression
• ``Local vs. ``global parameters -- breaking the Gaussian complexity barrier
• Sub-Gaussian estimators of the mean of a random vector
• Regularization and the small-ball method. I: Sparse recovery
• Slope meets Lasso: improved oracle bounds and optimality
• Learning from MOM's principles: Le Cam's approach
• On aggregation for heavy-tailed classes
• Regularization, sparse recovery, and median-of-means tournaments
• Learning without Concentration
• An Unrestricted Learning Procedure
• On Multiplier Processes Under Weak Moment Assumptions