mlsanityData to 7 Oct 2026

Robust Regression via Mutivariate Regression Depth

arXiv 1702.04656 ↗First posted 15 Feb 2017math.ST stat.ML stat.THcited by 20

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Abstract (arXiv)

This paper studies robust regression in the settings of Huber's ε-contamination models. We consider estimators that are maximizers of multivariate regression depth functions. These estimators are shown to achieve minimax rates in the settings of ε-contamination models for various regression problems including nonparametric regression, sparse linear regression, reduced rank regression, etc. We also discuss a general notion of depth function for linear operators that has potential applications in robust functional linear regression.

Key facts. Cited by 20 papers in the map (data through 7 Oct 2026). First posted on arXiv 15 Feb 2017.

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Citing papers per year: 2021: 3; 2022: 8; 2023: 3; 2024: 3; 2025: 2; 2026: 1.

20 papers.

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  1. 2021Robust and Differentially Private Mean Estimationcited by 66
  2. 2021Differential privacy and robust statistics in high dimensionscited by 64
  3. 2023From Robustness to Privacy and Backcited by 27
  4. 2022Trimmed Maximum Likelihood Estimation for Robust Learning in Generalized Linear Modelscited by 6
  5. 2022Robust and Sparse Estimation of Linear Regression Coefficients with Heavy-tailed Noises and Covariatescited by 6
  6. 2022Efficient List-Decodable Regression using Batchescited by 5
  7. 2022Outlier Robust and Sparse Estimation of Linear Regression Coefficientscited by 4
  8. 2022Robust supervised learning with coordinate gradient descentcited by 3
  9. 2022Robust Estimation for Nonparametric Families via Generative Adversarial Networkscited by 3
  10. 2022Differentially Private Estimation via Statistical Depthcited by 3
  11. 2023Linear Regression using Heterogeneous Data Batchescited by 3
  12. 2024Robust Second-Order Nonconvex Optimization and Its Application to Low Rank Matrix Sensingcited by 2
8 more
  1. 2021Robust Generalized Method of Moments: A Finite Sample Viewpointcited by 1
  2. 2024A Sample Efficient Alternating Minimization-based Algorithm For Robust Phase Retrievalcited by 1
  3. 2022A spectral least-squares-type method for heavy-tailed corrupted regression with unknown covariance & heterogeneous noisecited by 0
  4. 2023Calibrated Data-Dependent Constraints with Exact Satisfaction Guaranteescited by 0
  5. 2024Iterative thresholding for non-linear learning in the strong varepsilon-contamination modelcited by 0
  6. 2025Robust Estimation Under Heterogeneous Corruption Ratescited by 0
  7. 2025Robust and Sparse Estimation of Unbounded Density Ratio under Heavy Contaminationcited by 0
  8. 2026Robust Regression with Adaptive Contamination in Response: Optimal Rates and Computational Barrierscited by 0