mlsanityData to 14 Oct 2026

Robust Nonparametric Regression under Poisoning Attack

arXiv 2305.16771 ↗First posted 26 May 2023math.ST cs.CR cs.LGcited by 11

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Abstract (arXiv)

This paper studies robust nonparametric regression, in which an adversarial attacker can modify the values of up to q samples from a training dataset of size N. Our initial solution is an M-estimator based on Huber loss minimization. Compared with simple kernel regression, i.e. the Nadaraya-Watson estimator, this method can significantly weaken the impact of malicious samples on the regression performance. We provide the convergence rate as well as the corresponding minimax lower bound. The result shows that, with proper bandwidth selection, ℓ_∞ error is minimax optimal. The ℓ2 error is optimal with relatively small q, but is suboptimal with larger q. The reason is that this estimator is vulnerable if there are many attacked samples concentrating in a small region. To address this issue, we propose a correction method by projecting the initial estimate to the space of Lipschitz functions. The final estimate is nearly minimax optimal for arbitrary q, up to a ln N factor.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 28 of its 62 references that are in the map. First posted on arXiv 26 May 2023.

Builds on

28 of 62 references.

References · 28

  1. 2014Explaining and Harnessing Adversarial Examplescited by 7,364
  2. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
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  4. 2017Understanding Black-box Predictions via Influence Functionscited by 1,741
  5. 2017MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labelscited by 653
  6. 2020Learning from Noisy Labels with Deep Neural Networks: A Surveycited by 582
  7. 2017Certified Defenses for Data Poisoning Attackscited by 303
  8. 2018Manipulating Machine Learning: Poisoning Attacks and Countermeasures for Regression Learningcited by 225
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  11. 2015Learning with Symmetric Label Noise: The Importance of Being Unhingedcited by 120
  12. 2019Recent Advances in Algorithmic High-Dimensional Robust Statisticscited by 101
16 more
  1. 2018Is feature selection secure against training data poisoning?cited by 93
  2. 2017Being Robust (in High Dimensions) Can Be Practicalcited by 83
  3. 2017Mixture Models, Robustness, and Sum of Squares Proofscited by 81
  4. 2019Metric Learning for Adversarial Robustnesscited by 77
  5. 2018Robust Estimation via Robust Gradient Estimationcited by 76
  6. 2018Efficient Algorithms and Lower Bounds for Robust Linear Regressioncited by 76
  7. 2020Robust Linear Regression: Optimal Rates in Polynomial Timecited by 42
  8. 2019Faster Algorithms for High-Dimensional Robust Covariance Estimationcited by 28
  9. 2020Analysis of KNN Density Estimationcited by 28
  10. 2016Loss factorization, weakly supervised learning and label noise robustnesscited by 24
  11. 2022Overparameterized Linear Regression under Adversarial Attackscited by 21
  12. 2021Robust Regression Revisited: Acceleration and Improved Estimation Ratescited by 15
  13. 2019Fast Rates for a kNN Classifier Robust to Unknown Asymmetric Label Noisecited by 11
  14. 2019Minimax Rate Optimal Adaptive Nearest Neighbor Classification and Regressioncited by 11
  15. 2022Robust nonparametric regression: review and practical considerationscited by 4
  16. 2019The Trimmed Mean in Non-parametric Regression Function Estimationcited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 2; 2024: 4; 2025: 3; 2026: 2.

11 papers.

  1. 2023A Huber Loss Minimization Approach to Byzantine Robust Federated Learningcited by 16
  2. 2024A Huber Loss Minimization Approach to Mean Estimation under User-level Differential Privacycited by 11
  3. 2023Minimax Optimal Q Learning with Nearest Neighborscited by 8
  4. 2024Contextual Bandits for Unbounded Context Distributionscited by 8
  5. 2024BadCLM: Backdoor Attack in Clinical Language Models for Electronic Health Recordscited by 5
  6. 2025Credit Risk Identification in Supply Chains Using Generative Adversarial Networkscited by 5
  7. 2024Minimax rates of convergence for nonparametric regression under adversarial attackscited by 2
  8. 2025Adversarial Robustness of Nonparametric Regressioncited by 1
  9. 2026Safety-Efficacy Trade Off: Robustness against Data-Poisoningcited by 1
  10. 2025Analysis of the vulnerability of machine learning regression models to adversarial attacks using data from 5G wireless networkscited by 0
  11. 2026Adversarial Robustness of NTK Neural Networkscited by 0