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Empirical risk minimization for heavy-tailed losses

arXiv 1406.2462 ↗First posted 10 Jun 2014stat.MEcited by 37

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Abstract (arXiv)

The purpose of this paper is to discuss empirical risk minimization when the losses are not necessarily bounded and may have a distribution with heavy tails. In such situations, usual empirical averages may fail to provide reliable estimates and empirical risk minimization may provide large excess risk. However, some robust mean estimators proposed in the literature may be used to replace empirical means. In this paper, we investigate empirical risk minimization based on a robust estimate proposed by Catoni. We develop performance bounds based on chaining arguments tailored to Catoni's mean estimator.

Key facts. Cited by 37 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Jun 2014.

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Citing papers per year: 2021: 10; 2022: 13; 2023: 4; 2024: 2; 2025: 5; 2026: 3.

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  1. 2023Dynamic Regularized Sharpness Aware Minimization in Federated Learning: Approaching Global Consistency and Smooth Landscapecited by 46
  2. 2021High Dimensional Differentially Private Stochastic Optimization with Heavy-tailed Datacited by 42
  3. 2021Stability and Generalization of Stochastic Gradient Methods for Minimax Problemscited by 35
  4. 2022Rank-based Decomposable Losses in Machine Learning: A Surveycited by 26
  5. 2021Distribution-Free Robust Linear Regressioncited by 19
  6. 2021Uniform Concentration Bounds toward a Unified Framework for Robust Clusteringcited by 10
  7. 2022Robust Imitation Learning from Corrupted Demonstrationscited by 10
  8. 2021On the benefits of maximum likelihood estimation for Regression and Forecastingcited by 8
  9. 2022Quantizing Heavy-tailed Data in Statistical Estimation: (Near) Minimax Rates, Covariate Quantization, and Uniform Recoverycited by 7
  10. 2022Non-Asymptotic Guarantees for Robust Statistical Learning under Infinite Variance Assumptioncited by 6
  11. 2023On Regression in Extreme Regionscited by 6
  12. 2021A Survey of Learning Criteria Going Beyond the Usual Riskcited by 4
25 more
  1. 2022Robust Matrix Completion with Heavy-tailed Noisecited by 4
  2. 2025Improved Regret Bounds for Linear Bandits with Heavy-Tailed Rewardscited by 4
  3. 2022Robust supervised learning with coordinate gradient descentcited by 3
  4. 2022On Medians of (Randomized) Pairwise Meanscited by 3
  5. 2025Regularized least squares learning with heavy-tailed noise is minimax optimalcited by 3
  6. 2021Bandwidth-based Step-Sizes for Non-Convex Stochastic Optimizationcited by 2
  7. 2021Posterior concentration and fast convergence rates for generalized Bayesian learningcited by 2
  8. 2022Error Bound of Empirical ℓ2 Risk Minimization for Noisy Standard and Generalized Phase Retrieval Problemscited by 2
  9. 2022Tailoring to the Tails: Risk Measures for Fine-Grained Tail Sensitivitycited by 2
  10. 2022Distributional Robustness Bounds Generalization Errorscited by 2
  11. 2025On the Robustness of Kernel Ridge Regression Using the Cauchy Loss Functioncited by 2
  12. 2021Robust Generalized Method of Moments: A Finite Sample Viewpointcited by 1
  13. 2024Robust Mixture Learning when Outliers Overwhelm Small Groupscited by 1
  14. 2025Differentially Private Sparse Linear Regression with Heavy-tailed Responsescited by 1
  15. 2026Stability beyond Bounded Differences: Sharp Generalization Bounds under Finite Lp Momentscited by 1
  16. 2021Robust learning with anytime-guaranteed feedbackcited by 0
  17. 2022Robust Linear Predictions: Analyses of Uniform Concentration, Fast Rates and Model Misspecificationcited by 0
  18. 2022Efficient Private SCO for Heavy-Tailed Data via Averaged Clippingcited by 0
  19. 2022Robust High-dimensional Tuning Free Multiple Testingcited by 0
  20. 2023Robust variance-regularized risk minimization with concomitant scalingcited by 0
  21. 2023Empirical Risk Minimization for Losses without Variancecited by 0
  22. 2024Subsampled Ensemble Can Improve Generalization Tail Exponentiallycited by 0
  23. 2025Understanding Robust Machine Learning for Nonparametric Regression with Heavy-Tailed Noisecited by 0
  24. 2026Bilateral Trade Under Heavy-Tailed Valuations: Minimax Regret without a Variance Boundcited by 0
  25. 2026Median-of-Means as an Extremal Convex Estimator and a Nonconvex Route to the Trimmed Oraclecited by 0