mlsanityData to 7 Oct 2026

Outlier-robust estimation of a sparse linear model using ℓ1-penalized Huber's M-estimator

arXiv 1904.06288 ↗First posted 12 Apr 2019math.ST cs.LG stat.THcited by 31

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Abstract (arXiv)

We study the problem of estimating a p-dimensional s-sparse vector in a linear model with Gaussian design and additive noise. In the case where the labels are contaminated by at most o adversarial outliers, we prove that the ℓ1-penalized Huber's M-estimator based on n samples attains the optimal rate of convergence (s/n)1/2 + (o/n), up to a logarithmic factor. For more general design matrices, our results highlight the importance of two properties: the transfer principle and the incoherence property. These properties with suitable constants are shown to yield the optimal rates, up to log-factors, of robust estimation with adversarial contamination.

Key facts. Cited by 31 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Apr 2019.

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Citing papers per year: 2021: 4; 2022: 10; 2023: 7; 2024: 3; 2025: 5; 2026: 2.

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  1. 2021Robust and Differentially Private Mean Estimationcited by 66
  2. 2021Consistent Estimation for PCA and Sparse Regression with Oblivious Outlierscited by 9
  3. 2023Near Optimal Private and Robust Linear Regressioncited by 9
  4. 2021Kalman Filtering with Adversarial Corruptionscited by 6
  5. 2022Bandits Corrupted by Nature: Lower Bounds on Regret and Robust Optimistic Algorithmcited by 6
  6. 2022Robust and Sparse Estimation of Linear Regression Coefficients with Heavy-tailed Noises and Covariatescited by 6
  7. 2022Robust Methods for High-Dimensional Linear Learningcited by 5
  8. 2022Efficient List-Decodable Regression using Batchescited by 5
  9. 2022Outlier Robust and Sparse Estimation of Linear Regression Coefficientscited by 4
  10. 2023Linear Regression using Heterogeneous Data Batchescited by 3
  11. 2025A Piecewise Lyapunov Analysis of Sub-quadratic SGD: Applications to Robust and Quantile Regressioncited by 2
  12. 2025Heavy Lasso: sparse penalized regression under heavy-tailed noise via data-augmented soft-thresholdingcited by 2
19 more
  1. 2022Minimax rate of consistency for linear models with missing valuescited by 1
  2. 2022Robust Linear Regression for General Feature Distributioncited by 1
  3. 2022Nearly minimax robust estimator of the mean vector by iterative spectral dimension reductioncited by 1
  4. 2022Stochastic Mirror Descent for Large-Scale Sparse Recoverycited by 1
  5. 2023Asymptotic Characterisation of Robust Empirical Risk Minimisation Performance in the Presence of Outlierscited by 1
  6. 2023Outlier-robust Estimation of a Sparse Linear Model Using Invexitycited by 1
  7. 2023Distribution-Independent Regression for Generalized Linear Models with Oblivious Corruptionscited by 1
  8. 2024Robust Sparse Regression with Non-Isotropic Designscited by 1
  9. 2026Outlier-Robust Diffusion Solvers for Inverse Problemscited by 1
  10. 2021Adversarial robust weighted Huber regressioncited by 0
  11. 2022A spectral least-squares-type method for heavy-tailed corrupted regression with unknown covariance & heterogeneous noisecited by 0
  12. 2023Sparse Recovery with Shuffled Labels: Statistical Limits and Practical Estimatorscited by 0
  13. 2023Estimation of sparse linear regression coefficients under L-subexponential covariatescited by 0
  14. 2024Purification Of Contaminated Convolutional Neural Networks Via Robust Recovery: An Approach with Theoretical Guarantee in One-Hidden-Layer Casecited by 0
  15. 2024Sparse Linear Regression when Noises and Covariates are Heavy-Tailed and Contaminated by Outlierscited by 0
  16. 2025On robust recovery of signals from indirect observationscited by 0
  17. 2025Lasso and Partially-Rotated Designscited by 0
  18. 2025Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contaminationcited by 0
  19. 2026Robust Regression with Adaptive Contamination in Response: Optimal Rates and Computational Barrierscited by 0