mlsanityData to 7 Oct 2026

Trimmed Maximum Likelihood Estimation for Robust Learning in Generalized Linear Models

arXiv 2206.04777 ↗First posted 9 Jun 2022cs.LG stat.MLcited by 6

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Abstract (arXiv)

We study the problem of learning generalized linear models under adversarial corruptions. We analyze a classical heuristic called the iterative trimmed maximum likelihood estimator which is known to be effective against label corruptions in practice. Under label corruptions, we prove that this simple estimator achieves minimax near-optimal risk on a wide range of generalized linear models, including Gaussian regression, Poisson regression and Binomial regression. Finally, we extend the estimator to the more challenging setting of label and covariate corruptions and demonstrate its robustness and optimality in that setting as well.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 25 of its 54 references that are in the map. First posted on arXiv 9 Jun 2022.

Builds on

25 of 54 references.

References · 25

  1. 2016Robust Estimators in High Dimensions without the Computational Intractabilitycited by 209
  2. 2016Agnostic Estimation of Mean and Covariancecited by 131
  3. 2019Recent Advances in Algorithmic High-Dimensional Robust Statisticscited by 100
  4. 2016Learning from Untrusted Datacited by 90
  5. 2018Robust Estimation via Robust Gradient Estimationcited by 76
  6. 2018Efficient Algorithms and Lower Bounds for Robust Linear Regressioncited by 76
  7. 2018Efficient Algorithms for Outlier-Robust Regressioncited by 72
  8. 2020Outlier Robust Mean Estimation with Subgaussian Rates via Stabilitycited by 50
  9. 2020Robust regression with covariate filtering: Heavy tails and adversarial contaminationcited by 49
  10. 2017Resilience: A Criterion for Learning in the Presence of Arbitrary Outlierscited by 43
  11. 2020Robust Linear Regression: Optimal Rates in Polynomial Timecited by 42
  12. 2019Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier Detectioncited by 41
13 more
  1. 2015Robust Regression via Hard Thresholdingcited by 39
  2. 2019Generalized Resilience and Robust Statisticscited by 37
  3. 2020Robust Sub-Gaussian Principal Component Analysis and Width-Independent Schatten Packingcited by 35
  4. 2020Optimal Robust Linear Regression in Nearly Linear Timecited by 31
  5. 2020Online and Distribution-Free Robustness: Regression and Contextual Bandits with Huber Contaminationcited by 26
  6. 2019Adaptive Hard Thresholding for Near-optimal Consistent Robust Regressioncited by 23
  7. 2017Robust Regression via Mutivariate Regression Depthcited by 20
  8. 2020Robust estimation via generalized quasi-gradientscited by 19
  9. 2020High-Dimensional Robust Mean Estimation via Gradient Descentcited by 16
  10. 2021Robust Regression Revisited: Acceleration and Improved Estimation Ratescited by 15
  11. 2021Outlier-Robust Learning of Ising Models Under Dobrushin's Conditioncited by 14
  12. 2021Outlier-Robust Sparse Estimation via Non-Convex Optimizationcited by 14
  13. 2019Iterative Least Trimmed Squares for Mixed Linear Regressioncited by 13

Built on by

Cited by year (2026 to 7 Oct)

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

6 papers.

  1. 2024RobustTSF: Towards Theory and Design of Robust Time Series Forecasting with Anomaliescited by 17
  2. 2023Near Optimal Private and Robust Linear Regressioncited by 9
  3. 2025A Unified Theoretical Analysis of Private and Robust Offline Alignment: from RLHF to DPOcited by 8
  4. 2022Efficient List-Decodable Regression using Batchescited by 5
  5. 2023Linear Regression using Heterogeneous Data Batchescited by 3
  6. 2026Convex Basins in Single-Index Model Loss Landscapes: Applications to Robust Recovery under Strong Adversarial Corruptioncited by 0