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Adaptive Huber Regression

arXiv 1706.06991 ↗First posted 21 Jun 2017math.ST stat.ME stat.THcited by 60

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Abstract (arXiv)

Big data can easily be contaminated by outliers or contain variables with heavy-tailed distributions, which makes many conventional methods inadequate. To address this challenge, we propose the adaptive Huber regression for robust estimation and inference. The key observation is that the robustification parameter should adapt to the sample size, dimension and moments for optimal tradeoff between bias and robustness. Our theoretical framework deals with heavy-tailed distributions with bounded (1+δ)-th moment for any δ > 0. We establish a sharp phase transition for robust estimation of regression parameters in both low and high dimensions: when δ ≥ 1, the estimator admits a sub-Gaussian-type deviation bound without sub-Gaussian assumptions on the data, while only a slower rate is available in the regime 0<δ< 1. Furthermore, this transition is smooth and optimal. In addition, we extend the methodology to allow both heavy-tailed predictors and observation noise. Simulation studies lend further support to the theory. In a genetic study of cancer cell lines that exhibit heavy-tailedness, the proposed methods are shown to be more robust and predictive.

Key facts. Cited by 60 papers in the map (data through 14 Oct 2026). First posted on arXiv 21 Jun 2017.

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Citing papers per year: 2021: 8; 2022: 15; 2023: 13; 2024: 5; 2025: 5; 2026: 14.

60 papers.

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  1. 2022How do noise tails impact on deep ReLU networks?cited by 25
  2. 2023Towards Robust Offline Reinforcement Learning under Diverse Data Corruptioncited by 24
  3. 2023High-dimensional robust regression under heavy-tailed data: Asymptotics and Universalitycited by 15
  4. 2022Data-Driven Sample Average Approximation with Covariate Informationcited by 14
  5. 2023Tackling Heavy-Tailed Rewards in Reinforcement Learning with Function Approximation: Minimax Optimal and Instance-Dependent Regret Boundscited by 14
  6. 2022High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantizationcited by 13
  7. 2021Heavy-tailed Streaming Statistical Estimationcited by 10
  8. 2021Communication-Constrained Distributed Quantile Regression with Optimal Statistical Guaranteescited by 8
  9. 2023Variance-aware robust reinforcement learning with linear function approximation under heavy-tailed rewardscited by 8
  10. 2024Low-rank Matrix Bandits with Heavy-tailed Rewardscited by 7
  11. 2022Non-Asymptotic Guarantees for Robust Statistical Learning under Infinite Variance Assumptioncited by 6
  12. 2022Higher degree sum-of-squares relaxations robust against oblivious outlierscited by 6
38 more
  1. 2021Heteroscedasticity-aware residuals-based contextual stochastic optimizationcited by 5
  2. 2022Are Latent Factor Regression and Sparse Regression Adequate?cited by 5
  3. 2022Forecasting SQL Query Cost at Twittercited by 5
  4. 2025Heavy-Tailed Linear Bandits: Huber Regression with One-Pass Updatecited by 5
  5. 2022Robust Matrix Completion with Heavy-tailed Noisecited by 4
  6. 2022Outlier Robust and Sparse Estimation of Linear Regression Coefficientscited by 4
  7. 2023Computationally Efficient and Statistically Optimal Robust High-Dimensional Linear Regressioncited by 4
  8. 2023Online Estimation and Inference for Robust Policy Evaluation in Reinforcement Learningcited by 4
  9. 2023Improved Analysis of Sparse Linear Regression in Local Differential Privacy Modelcited by 4
  10. 2025Improved Regret Bounds for Linear Bandits with Heavy-Tailed Rewardscited by 4
  11. 2021A Survey Of Regression Algorithms And Connections With Deep Learningcited by 1
  12. 2021Non-asymptotic analysis and inference for an outlyingness induced winsorized meancited by 1
  13. 2021Robust Variable Selection and Estimation Via Adaptive Elastic Net S-Estimators for Linear Regressioncited by 1
  14. 2022Robust Linear Regression for General Feature Distributioncited by 1
  15. 2022Click prediction boosting via Bayesian hyperparameter optimization based ensemble learning pipelinescited by 1
  16. 2022Robust convex biclustering with a tuning-free methodcited by 1
  17. 2023Outlier-robust Estimation of a Sparse Linear Model Using Invexitycited by 1
  18. 2025Differentially Private Sparse Linear Regression with Heavy-tailed Responsescited by 1
  19. 2021Predictive models for wind speed using artificial intelligence and copulacited by 0
  20. 2021Markov subsampling based Huber Criterioncited by 0
  21. 2022Robust High-dimensional Tuning Free Multiple Testingcited by 0
  22. 2022Retire: Robust Expectile Regression in High Dimensionscited by 0
  23. 2022Mining the Factor Zoo: Estimation of Latent Factor Models with Sufficient Proxiescited by 0
  24. 2023Robust Mean Estimation Without Moments for Symmetric Distributionscited by 0
  25. 2023The Adaptive τ-Lasso: Robustness and Oracle Propertiescited by 0
  26. 2023Estimation of sparse linear regression coefficients under L-subexponential covariatescited by 0
  27. 2023Robust penalized least squares of depth trimmed residuals regression for high-dimensional datacited by 0
  28. 2023High-Quality Live Video Streaming via Transcoding Time Prediction and Preset Selectioncited by 0
  29. 2024Regularized Projection Matrix Approximation with Applications to Community Detectioncited by 0
  30. 2024Sparse Linear Regression when Noises and Covariates are Heavy-Tailed and Contaminated by Outlierscited by 0
  31. 2024Residual-based Adaptive Huber Loss (RAHL) -- Design of an improved Huber loss for CQI prediction in 5G networkscited by 0
  32. 2024Adaptive and Stratified Subsampling for High-Dimensional Robust Estimationcited by 0
  33. 2025LARP: Learner-Agnostic Robust Data Prefilteringcited by 0
  34. 2025Efficient Group Lasso Regularized Rank Regression with Simulation-Based Tuningcited by 0
  35. 2026Development of Domain-Invariant Visual Enhancement and Restoration (DIVER) Approach for Underwater Imagescited by 0
  36. 2026Robust and Computationally Efficient Linear Contextual Bandits under Adversarial Corruption and Heavy-Tailed Noisecited by 0
  37. 2026A Robust Low-Rank Prior Model for Structured Cartoon-Texture Image Decomposition with Heavy-Tailed Noisecited by 0
  38. 2026Robust Tensor Regression with Nonconvexity: Algorithmic and Statistical Theorycited by 0

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