Air-HOLP: Adaptive Regularized Feature Screening for High Dimensional Correlated Data
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| Format: | Preprint |
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2024
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| _version_ | 1866913722900938752 |
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| author | Joudah, Ibrahim Muller, Samuel Zhu, Houying |
| author_facet | Joudah, Ibrahim Muller, Samuel Zhu, Houying |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2408_13000 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Air-HOLP: Adaptive Regularized Feature Screening for High Dimensional Correlated Data Joudah, Ibrahim Muller, Samuel Zhu, Houying Methodology Computation 62J07 (Primary) 62H20, 62J05 (Secondary) 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. |
| title | Air-HOLP: Adaptive Regularized Feature Screening for High Dimensional Correlated Data |
| topic | Methodology Computation 62J07 (Primary) 62H20, 62J05 (Secondary) |
| url | https://arxiv.org/abs/2408.13000 |