mlsanityData to 7 Oct 2026

Outlier Robust and Sparse Estimation of Linear Regression Coefficients

arXiv 2208.11592 ↗First posted 24 Aug 2022math.ST stat.ML stat.THcited by 4

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Abstract (arXiv)

We consider outlier-robust and sparse estimation of linear regression coefficients, when the covariates and the noises are contaminated by adversarial outliers and noises are sampled from a heavy-tailed distribution. Our results present sharper error bounds under weaker assumptions than prior studies that share similar interests with this study. Our analysis relies on some sharp concentration inequalities resulting from generic chaining.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 37 of its 90 references that are in the map. First posted on arXiv 24 Aug 2022.

Builds on

37 of 90 references.

References · 37

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25 more
  1. 2020Robust Linear Regression: Optimal Rates in Polynomial Timecited by 42
  2. 2019Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier Detectioncited by 41
  3. 2017Robustly Learning a Gaussian: Getting Optimal Error, Efficientlycited by 39
  4. 2018High-Dimensional Robust Mean Estimation in Nearly-Linear Timecited by 39
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  6. 2019Outlier-robust estimation of a sparse linear model using ℓ1-penalized Huber's M-estimatorcited by 31
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  17. 2014Learning without Concentration for General Loss Functionscited by 13
  18. 2013Sparse Representation of a Polytope and Recovery of Sparse Signals and Low-rank Matricescited by 8
  19. 2018Learning Compact Neural Networks with Regularizationcited by 8
  20. 2019Robust Inference via Multiplier Bootstrapcited by 8
  21. 2020Generic Error Bounds for the Generalized Lasso with Sub-Exponential Datacited by 6
  22. 2020Outlier-robust sparse/low-rank least-squares regression and robust matrix completioncited by 6
  23. 2022Robust and Sparse Estimation of Linear Regression Coefficients with Heavy-tailed Noises and Covariatescited by 6
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  25. 2022Robust Methods for High-Dimensional Linear Learningcited by 5

Built on by

Cited by year (2026 to 7 Oct)

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

4 papers.

  1. 2025Non-Asymptotic Analysis of Efficiency in Conformalized Regressioncited by 2
  2. 2024Robust Sparse Regression with Non-Isotropic Designscited by 1
  3. 2024Sparse Linear Regression when Noises and Covariates are Heavy-Tailed and Contaminated by Outlierscited by 0
  4. 2026Virtual Dummies: Enabling Scalable FDR-Controlled Variable Selection via Sequential Sampling of Null Featurescited by 0