# Adversarial Contamination Meets Hard Thresholding: An Iterative Algorithm with Signal Adaptivity and Minimax Optimality

arXiv: https://arxiv.org/abs/2606.27685 · HTML: https://mlsanity.com/paper/2606.27685/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 53 references that are in the map.
- First posted on arXiv 26 Jun 2026.

## Builds on (most cited first, 2 of 2)

- [Outlier-robust sparse/low-rank least-squares regression and robust matrix completion](https://mlsanity.com/paper/2012.06750/) (2020)
- [Robust estimation with Lasso when outputs are adversarially contaminated](https://mlsanity.com/paper/2004.05990/) (2020)

## Abstract (arXiv)

Pervasive data contamination -- stemming from measurement errors, outliers, or adversarial corruption -- has motivated the development of robust statistical methods. In this context, we propose a two-stage Adversarial Contamination-resistant Iterative Hard Thresholding (AC-IHT) algorithm for high-dimensional regression with contamination. Our nonconvex algorithm achieves minimax near-optimal (up to logarithmic terms) estimation by iteratively updating the coefficient vector and the contamination vector with different thresholding scales. We further demonstrate that our AC-IHT estimator is signal-adaptive: under proper signal conditions, it adaptively attains a sharper estimation rate and more accurate support recovery. Moreover, it enjoys the strong oracle property, laying a theoretical foundation for asymptotic inference. Numerical experiments confirm its superior finite-sample performance. Finally, we discuss theoretical extensions of the proposed procedure to generalized linear models and to heavy-tailed noise settings.