mlsanityData to 7 Oct 2026

Non-Asymptotic Guarantees for Robust Statistical Learning under Infinite Variance Assumption

arXiv 2201.03182 ↗First posted 10 Jan 2022stat.ML cs.LG math.STcited by 6

Not on the map. Why?

Abstract (arXiv)

There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust estimators, the ridge log-truncated M-estimator and the elastic net log-truncated M-estimator. The first estimator is applied to convex regressions such as quantile regression and generalized linear models, while the other one is applied to high dimensional non-convex learning problems such as regressions via deep neural networks. Simulations and real data analysis demonstrate the {robustness} of log-truncated estimations over standard estimations.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 26 of its 62 references that are in the map. First posted on arXiv 10 Jan 2022.

Builds on

26 of 62 references.

References · 26

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2018The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networkscited by 2,250
  3. 2017Nonparametric regression using deep neural networks with ReLU activation functioncited by 431
  4. 2019Mean estimation and regression under heavy-tailed distributions--a surveycited by 133
  5. 2016The Landscape of Empirical Risk for Non-convex Lossescited by 86
  6. 2017Adaptive Huber Regressioncited by 59
  7. 2014Empirical risk minimization for heavy-tailed lossescited by 37
  8. 2019A Selective Overview of Deep Learningcited by 31
  9. 2018Finite-sample analysis of M-estimators using self-concordancecited by 30
  10. 2015Statistical consistency and asymptotic normality for high-dimensional robust M-estimatorscited by 27
  11. 2020Statistical Guarantees for Regularized Neural Networkscited by 25
  12. 2020Quantile regression with deep ReLU Networks: Estimators and minimax ratescited by 24
14 more
  1. 2020Bridging Convex and Nonconvex Optimization in Robust PCA: Noise, Outliers, and Missing Datacited by 23
  2. 2020Nonconvex sparse regularization for deep neural networks and its optimalitycited by 21
  3. 2017Estimating the Coefficients of a Mixture of Two Linear Regressions by Expectation Maximizationcited by 19
  4. 2016Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entriescited by 18
  5. 2020Optimal Algorithms for Stochastic Multi-Armed Bandits with Heavy Tailed Rewardscited by 18
  6. 2019Lecture Notes: Selected topics on robust statistical learning theorycited by 17
  7. 2018Convergence guarantees for a class of non-convex and non-smooth optimization problemscited by 15
  8. 2019Truncated Cauchy Non-negative Matrix Factorizationcited by 11
  9. 2019Excess risk bounds in robust empirical risk minimizationcited by 9
  10. 2020Risk Bounds for Robust Deep Learningcited by 9
  11. 2017Elastic-net Regularized High-dimensional Negative Binomial Regression: Consistency and Weak Signals Detectioncited by 8
  12. 2018Learning with Non-Convex Truncated Losses by SGDcited by 7
  13. 2021Do we need to estimate the variance in robust mean estimation?cited by 6
  14. 2021Non-asymptotic Excess Risk Bounds for Classification with Deep Convolutional Neural Networkscited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 0; 2024: 2; 2025: 1; 2026: 2.

6 papers.

  1. 2024Robust deep learning from weakly dependent datacited by 5
  2. 2025On the Robustness of Kernel Ridge Regression Using the Cauchy Loss Functioncited by 2
  3. 2026Sharper Generalization Bounds for Transformercited by 2
  4. 2024Weak Robust Compatibility Between Learning Algorithms and Counterfactual Explanation Generation Algorithmscited by 1
  5. 2022Distribution Estimation of Contaminated Data via DNN-based MoM-GANscited by 0
  6. 2026Tail-Aware Information-Theoretic Bounds for LLM Alignment under Heavy-Tailed Rewardscited by 0