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Sparse Linear Regression when Noises and Covariates are Heavy-Tailed and Contaminated by Outliers

arXiv 2408.01336 ↗First posted 2 Aug 2024stat.ML cs.LGcited by 0

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Abstract (arXiv)

We investigate a problem estimating coefficients of linear regression under sparsity assumption when covariates and noises are sampled from heavy tailed distributions. Additionally, we consider the situation where not only covariates and noises are sampled from heavy tailed distributions but also contaminated by outliers. Our estimators can be computed efficiently, and exhibit sharp error bounds.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 21 of its 47 references that are in the map. First posted on arXiv 2 Aug 2024.

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21 of 47 references.

References · 21

  1. 2016Statistical Query Lower Bounds for Robust Estimation of High-dimensional Gaussians and Gaussian Mixturescited by 114
  2. 2017Adaptive Huber Regressioncited by 59
  3. 2020Statistical Query Algorithms and Low-Degree Tests Are Almost Equivalentcited by 51
  4. 2020Robust regression with covariate filtering: Heavy tails and adversarial contaminationcited by 49
  5. 2020Robust Linear Regression: Optimal Rates in Polynomial Timecited by 42
  6. 2019Subexponential-Time Algorithms for Sparse PCAcited by 41
  7. 2020Computational Barriers to Estimation from Low-Degree Polynomialscited by 38
  8. 2019Outlier-robust estimation of a sparse linear model using ℓ1-penalized Huber's M-estimatorcited by 31
  9. 2018High Dimensional Robust Sparse Regressioncited by 29
  10. 2014Statistical and computational trade-offs in estimation of sparse principal componentscited by 26
  11. 2016A Shrinkage Principle for Heavy-Tailed Data: High-Dimensional Robust Low-Rank Matrix Recoverycited by 23
  12. 2022Robust Sparse Mean Estimation via Sum of Squarescited by 23
9 more
  1. 2018User-Friendly Covariance Estimation for Heavy-Tailed Distributionscited by 15
  2. 2022Outlier-Robust Sparse Mean Estimation for Heavy-Tailed Distributionscited by 13
  3. 2020Computationally efficient sparse clusteringcited by 12
  4. 2019Robust Inference via Multiplier Bootstrapcited by 8
  5. 2023Statistical-Computational Tradeoffs in Mixed Sparse Linear Regressioncited by 7
  6. 2018Curse of Heterogeneity: Computational Barriers in Sparse Mixture Models and Phase Retrievalcited by 6
  7. 2020Generic Error Bounds for the Generalized Lasso with Sub-Exponential Datacited by 6
  8. 2022Robust Methods for High-Dimensional Linear Learningcited by 5
  9. 2022Outlier Robust and Sparse Estimation of Linear Regression Coefficientscited by 4

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