New AC-IHT Algorithm Resists Adversarial Data Contamination

Researchers Shixiang Liu and Hanming Yang have introduced AC-IHT (Adversarial Contamination-resistant Iterative Hard Thresholding), a two-stage nonconvex algorithm designed to tackle high-dimensional regression when data is corrupted by adversaries, outliers, or measurement errors. The algorithm works by iteratively updating the coefficient vector and the contamination vector using distinct thresholding scales, which allows it to handle up to a constant fraction of corrupted samples while maintaining statistical efficiency. The authors prove that AC-IHT achieves minimax near-optimal estimation error (up to logarithmic factors) and is signal-adaptive: under favorable signal conditions, it automatically attains a sharper estimation rate and more accurate support recovery. The estimator also satisfies the strong oracle property, meaning it performs as if the true support set were known, laying the groundwork for asymptotic inference.

The paper demonstrates through extensive numerical experiments that AC-IHT outperforms existing robust methods in finite-sample settings, particularly when contamination levels are high. The theoretical framework is further extended to generalized linear models (GLMs) and heavy-tailed noise distributions, broadening its applicability. This work is particularly relevant for modern machine learning pipelines where data integrity cannot be guaranteed, such as in federated learning, sensor networks, or security-sensitive applications. The algorithm's ability to automatically adapt to signal strength while providing theoretical guarantees makes it a promising tool for practitioners dealing with contaminated datasets.