# Trimmed Maximum Likelihood Estimation for Robust Learning in Generalized Linear Models

arXiv: https://arxiv.org/abs/2206.04777 · HTML: https://mlsanity.com/paper/2206.04777/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 54 references that are in the map.
- First posted on arXiv 9 Jun 2022.

## Builds on (most cited first, 25 of 25)

- [Robust Estimators in High Dimensions without the Computational Intractability](https://mlsanity.com/paper/1604.06443/) (2016)
- [Agnostic Estimation of Mean and Covariance](https://mlsanity.com/paper/1604.06968/) (2016)
- [Recent Advances in Algorithmic High-Dimensional Robust Statistics](https://mlsanity.com/paper/1911.05911/) (2019)
- [Learning from Untrusted Data](https://mlsanity.com/paper/1611.02315/) (2016)
- [Robust Estimation via Robust Gradient Estimation](https://mlsanity.com/paper/1802.06485/) (2018)
- [Efficient Algorithms and Lower Bounds for Robust Linear Regression](https://mlsanity.com/paper/1806.00040/) (2018)
- [Efficient Algorithms for Outlier-Robust Regression](https://mlsanity.com/paper/1803.03241/) (2018)
- [Outlier Robust Mean Estimation with Subgaussian Rates via Stability](https://mlsanity.com/paper/2007.15618/) (2020)
- [Robust regression with covariate filtering: Heavy tails and adversarial contamination](https://mlsanity.com/paper/2009.12976/) (2020)
- [Resilience: A Criterion for Learning in the Presence of Arbitrary Outliers](https://mlsanity.com/paper/1703.04940/) (2017)
- [Robust Linear Regression: Optimal Rates in Polynomial Time](https://mlsanity.com/paper/2007.01394/) (2020)
- [Quantum Entropy Scoring for Fast Robust Mean Estimation and Improved Outlier Detection](https://mlsanity.com/paper/1906.11366/) (2019)
- [Robust Regression via Hard Thresholding](https://mlsanity.com/paper/1506.02428/) (2015)
- [Generalized Resilience and Robust Statistics](https://mlsanity.com/paper/1909.08755/) (2019)
- [Robust Sub-Gaussian Principal Component Analysis and Width-Independent Schatten Packing](https://mlsanity.com/paper/2006.06980/) (2020)
- [Optimal Robust Linear Regression in Nearly Linear Time](https://mlsanity.com/paper/2007.08137/) (2020)
- [Online and Distribution-Free Robustness: Regression and Contextual Bandits with Huber Contamination](https://mlsanity.com/paper/2010.04157/) (2020)
- [Adaptive Hard Thresholding for Near-optimal Consistent Robust Regression](https://mlsanity.com/paper/1903.08192/) (2019)
- [Robust Regression via Mutivariate Regression Depth](https://mlsanity.com/paper/1702.04656/) (2017)
- [Robust estimation via generalized quasi-gradients](https://mlsanity.com/paper/2005.14073/) (2020)
- [High-Dimensional Robust Mean Estimation via Gradient Descent](https://mlsanity.com/paper/2005.01378/) (2020)
- [Robust Regression Revisited: Acceleration and Improved Estimation Rates](https://mlsanity.com/paper/2106.11938/) (2021)
- [Outlier-Robust Learning of Ising Models Under Dobrushin's Condition](https://mlsanity.com/paper/2102.02171/) (2021)
- [Outlier-Robust Sparse Estimation via Non-Convex Optimization](https://mlsanity.com/paper/2109.11515/) (2021)
- [Iterative Least Trimmed Squares for Mixed Linear Regression](https://mlsanity.com/paper/1902.03653/) (2019)

## Built on by (most cited first, 6 of 6)

- [RobustTSF: Towards Theory and Design of Robust Time Series Forecasting with Anomalies](https://mlsanity.com/paper/2402.02032/) (2024)
- [Near Optimal Private and Robust Linear Regression](https://mlsanity.com/paper/2301.13273/) (2023)
- [A Unified Theoretical Analysis of Private and Robust Offline Alignment: from RLHF to DPO](https://mlsanity.com/paper/2505.15694/) (2025)
- [Efficient List-Decodable Regression using Batches](https://mlsanity.com/paper/2211.12743/) (2022)
- [Linear Regression using Heterogeneous Data Batches](https://mlsanity.com/paper/2309.01973/) (2023)
- [Convex Basins in Single-Index Model Loss Landscapes: Applications to Robust Recovery under Strong Adversarial Corruption](https://mlsanity.com/paper/2605.29497/) (2026)

## 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.