# Air-HOLP: Adaptive Regularized Feature Screening for High Dimensional Correlated Data

arXiv: https://arxiv.org/abs/2408.13000 · HTML: https://mlsanity.com/paper/2408.13000/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Aug 2024.

## Built on by (most cited first, 3 of 3)

- [Stability Selection via Variable Decorrelation](https://mlsanity.com/paper/2505.20864/) (2025)
- [A Stable Lasso](https://mlsanity.com/paper/2511.02306/) (2025)
- [PACE: Plug-and-Play Contextual Embedding for Feature Screening with Pretrained Tabular Foundation Models](https://mlsanity.com/paper/2609.23574/) (2026)

## Abstract (arXiv)

Handling high-dimensional datasets presents substantial computational challenges, particularly when the number of features far exceeds the number of observations and when features are highly correlated. A modern approach to mitigate these issues is feature screening. In this work, the High-dimensional Ordinary Least-squares Projection (HOLP) feature screening method is advanced by employing adaptive ridge regularization. The impact of the ridge tuning parameter on the Ridge-HOLP method is examined and Adaptive iterative ridge-HOLP (Air-HOLP) is proposed, a data-adaptive advance to Ridge-HOLP where the ridge-regularization tuning parameter is selected iteratively and optimally for better feature screening performance. The proposed method addresses the challenges of tuning parameter selection in high dimensions by offering a computationally efficient and stable alternative to traditional methods like bootstrapping and cross-validation. Air-HOLP is evaluated using simulated data and a prostate cancer genetic dataset. The empirical results demonstrate that Air-HOLP has improved performance over a large range of simulation settings. We provide R codes implementing the Air-HOLP feature screening method and integrating it into existing feature screening methods that utilize the HOLP formula.