# Corruption-tolerant Algorithms for Generalized Linear Models

arXiv: https://arxiv.org/abs/2212.05430 · HTML: https://mlsanity.com/paper/2212.05430/

## Key facts

- No citing papers in the map yet (data through 7 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 11 Dec 2022.

## Builds on (most cited first, 12 of 12)

- [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)
- [Sever: A Robust Meta-Algorithm for Stochastic Optimization](https://mlsanity.com/paper/1803.02815/) (2018)
- [Tilted Empirical Risk Minimization](https://mlsanity.com/paper/2007.01162/) (2020)
- [Recent Advances in Algorithmic High-Dimensional Robust Statistics](https://mlsanity.com/paper/1911.05911/) (2019)
- [Robust Estimation via Robust Gradient Estimation](https://mlsanity.com/paper/1802.06485/) (2018)
- [Learning with Confident Examples: Rank Pruning for Robust Classification with Noisy Labels](https://mlsanity.com/paper/1705.01936/) (2017)
- [Robust Regression via Hard Thresholding](https://mlsanity.com/paper/1506.02428/) (2015)
- [High-Dimensional Robust Mean Estimation in Nearly-Linear Time](https://mlsanity.com/paper/1811.09380/) (2018)
- [Adaptive Hard Thresholding for Near-optimal Consistent Robust Regression](https://mlsanity.com/paper/1903.08192/) (2019)
- [Globally-convergent Iteratively Reweighted Least Squares for Robust Regression Problems](https://mlsanity.com/paper/2006.14211/) (2020)
- [Robust Estimation in High Dimensional Generalized Linear Models](https://mlsanity.com/paper/1709.10261/) (2017)

## Abstract (arXiv)

This paper presents SVAM (Sequential Variance-Altered MLE), a unified framework for learning generalized linear models under adversarial label corruption in training data. SVAM extends to tasks such as least squares regression, logistic regression, and gamma regression, whereas many existing works on learning with label corruptions focus only on least squares regression. SVAM is based on a novel variance reduction technique that may be of independent interest and works by iteratively solving weighted MLEs over variance-altered versions of the GLM objective. SVAM offers provable model recovery guarantees superior to the state-of-the-art for robust regression even when a constant fraction of training labels are adversarially corrupted. SVAM also empirically outperforms several existing problem-specific techniques for robust regression and classification. Code for SVAM is available at https://github.com/purushottamkar/svam/