mlsanityData to 7 Oct 2026

Robust and Sparse Estimation of Linear Regression Coefficients with Heavy-tailed Noises and Covariates

arXiv 2206.07594 ↗First posted 15 Jun 2022stat.ML cs.LGcited by 6

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Abstract (arXiv)

Robust and sparse estimation of linear regression coefficients is investigated. The situation addressed by the present paper is that covariates and noises are sampled from heavy-tailed distributions, and the covariates and noises are contaminated by malicious outliers. Our estimator can be computed efficiently. Further, the error bound of the estimator is nearly optimal.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 32 of its 65 references that are in the map. First posted on arXiv 15 Jun 2022.

Builds on

32 of 65 references.

References · 32

  1. 2016Robust Estimators in High Dimensions without the Computational Intractabilitycited by 209
  2. 2016Agnostic Estimation of Mean and Covariancecited by 131
  3. 2019Recent Advances in Algorithmic High-Dimensional Robust Statisticscited by 100
  4. 2017Being Robust (in High Dimensions) Can Be Practicalcited by 83
  5. 2018Robust Estimation via Robust Gradient Estimationcited by 76
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  7. 2019Distribution-Independent PAC Learning of Halfspaces with Massart Noisecited by 54
  8. 2020Robust regression with covariate filtering: Heavy tails and adversarial contaminationcited by 49
  9. 2015Robust Covariance and Scatter Matrix Estimation under Huber's Contamination Modelcited by 47
  10. 2020Learning Halfspaces with Massart Noise Under Structured Distributionscited by 45
  11. 2020Robust Linear Regression: Optimal Rates in Polynomial Timecited by 42
  12. 2019Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier Detectioncited by 41
20 more
  1. 2017Robustly Learning a Gaussian: Getting Optimal Error, Efficientlycited by 39
  2. 2018High-Dimensional Robust Mean Estimation in Nearly-Linear Timecited by 39
  3. 2019Robust subgaussian estimation of a mean vector in nearly linear timecited by 37
  4. 2018Mean Estimation with Sub-Gaussian Rates in Polynomial Timecited by 33
  5. 2019Outlier-robust estimation of a sparse linear model using ℓ1-penalized Huber's M-estimatorcited by 31
  6. 2020Optimal Robust Linear Regression in Nearly Linear Timecited by 31
  7. 2018High Dimensional Robust Sparse Regressioncited by 29
  8. 2019Faster Algorithms for High-Dimensional Robust Covariance Estimationcited by 28
  9. 2014Statistical and computational trade-offs in estimation of sparse principal componentscited by 26
  10. 2016A Shrinkage Principle for Heavy-Tailed Data: High-Dimensional Robust Low-Rank Matrix Recoverycited by 23
  11. 2019Outlier-Robust High-Dimensional Sparse Estimation via Iterative Filteringcited by 23
  12. 2020Efficiently Learning Adversarially Robust Halfspaces with Noisecited by 22
  13. 2017Robust Regression via Mutivariate Regression Depthcited by 20
  14. 2019Fast Mean Estimation with Sub-Gaussian Ratescited by 18
  15. 2020The Complexity of Adversarially Robust Proper Learning of Halfspaces with Agnostic Noisecited by 15
  16. 2019A Fast Spectral Algorithm for Mean Estimation with Sub-Gaussian Ratescited by 12
  17. 2013Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-rank Matricescited by 8
  18. 2019Robust Inference via Multiplier Bootstrapcited by 8
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  20. 2019ERM and RERM are optimal estimators for regression problems when malicious outliers corrupt the labelscited by 5

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 1; 2024: 1; 2025: 0; 2026: 2.

6 papers.

  1. 2023High-dimensional robust regression under heavy-tailed data: Asymptotics and Universalitycited by 15
  2. 2022Robust Methods for High-Dimensional Linear Learningcited by 5
  3. 2022Outlier Robust and Sparse Estimation of Linear Regression Coefficientscited by 4
  4. 2024Robust Sparse Regression with Non-Isotropic Designscited by 1
  5. 2026Tractable Gaussian Phase Retrieval with Heavy Tails and Adversarial Corruption with Near-Linear Sample Complexitycited by 1
  6. 2026RobustLDS: Learning linear dynamical systems under adversarial corruptionscited by 0