Regularization, sparse recovery, and median-of-means tournaments
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Abstract (arXiv)
A regularized risk minimization procedure for regression function estimation is introduced that achieves near optimal accuracy and confidence under general conditions, including heavy-tailed predictor and response variables. The procedure is based on median-of-means tournaments, introduced by the authors in [8]. It is shown that the new procedure outperforms standard regularized empirical risk minimization procedures such as lasso or slope in heavy-tailed problems.
Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 Jan 2017.
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Citing papers per year: 2021: 5; 2022: 3; 2023: 2; 2024: 0; 2025: 1.
11 papers.
- 2021On Empirical Risk Minimization with Dependent and Heavy-Tailed Datacited by 16
- 2021Variance Reduced Median-of-Means Estimator for Byzantine-Robust Distributed Inferencecited by 11
- 2021Uniform Concentration Bounds toward a Unified Framework for Robust Clusteringcited by 10
- 2022Byzantine-Robust Federated Linear Banditscited by 7
- 2022Robust Methods for High-Dimensional Linear Learningcited by 5
- 2021Robust Principal Component Analysis: A Median of Means Approachcited by 4
- 2023Computationally Efficient and Statistically Optimal Robust High-Dimensional Linear Regressioncited by 4
- 2021DeepMoM: Robust Deep Learning With Median-of-Meanscited by 2
- 2023Robust empirical risk minimization via Newton's methodcited by 1
- 2022Robust Linear Predictions: Analyses of Uniform Concentration, Fast Rates and Model Misspecificationcited by 0
- 2025Convex Clustering Redefined: Robust Learning with the Median of Means Estimatorcited by 0
- 2025Convex Clustering Redefined: Robust Learning with the Median of Means Estimator12 Nov 2025
- 2023Computationally Efficient and Statistically Optimal Robust High-Dimensional Linear Regression10 May 2023
- 2023Robust empirical risk minimization via Newton's method30 Jan 2023
- 2022Robust Methods for High-Dimensional Linear Learning10 Aug 2022
- 2022Byzantine-Robust Federated Linear Bandits3 Apr 2022
- 2022Robust Linear Predictions: Analyses of Uniform Concentration, Fast Rates and Model Misspecification6 Jan 2022
- 2021Uniform Concentration Bounds toward a Unified Framework for Robust Clustering27 Oct 2021
- 2021On Empirical Risk Minimization with Dependent and Heavy-Tailed Data6 Sep 2021
- 2021DeepMoM: Robust Deep Learning With Median-of-Means28 May 2021
- 2021Variance Reduced Median-of-Means Estimator for Byzantine-Robust Distributed Inference4 Mar 2021
- 2021Robust Principal Component Analysis: A Median of Means Approach5 Feb 2021