Post-Transfer Learning Statistical Inference in High-Dimensional Regression
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909594122452992 |
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| author | Tam, Nguyen Vu Khai My, Cao Huyen Duy, Vo Nguyen Le |
| author_facet | Tam, Nguyen Vu Khai My, Cao Huyen Duy, Vo Nguyen Le |
| contents | Transfer learning (TL) for high-dimensional regression (HDR) is an important problem in machine learning, particularly when dealing with limited sample size in the target task. However, there currently lacks a method to quantify the statistical significance of the relationship between features and the response in TL-HDR settings. In this paper, we introduce a novel statistical inference framework for assessing the reliability of feature selection in TL-HDR, called PTL-SI (Post-TL Statistical Inference). The core contribution of PTL-SI is its ability to provide valid $p$-values to features selected in TL-HDR, thereby rigorously controlling the false positive rate (FPR) at desired significance level $α$ (e.g., 0.05). Furthermore, we enhance statistical power by incorporating a strategic divide-and-conquer approach into our framework. We demonstrate the validity and effectiveness of the proposed PTL-SI through extensive experiments on both synthetic and real-world high-dimensional datasets, confirming its theoretical properties and utility in testing the reliability of feature selection in TL scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_18212 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Post-Transfer Learning Statistical Inference in High-Dimensional Regression Tam, Nguyen Vu Khai My, Cao Huyen Duy, Vo Nguyen Le Machine Learning Transfer learning (TL) for high-dimensional regression (HDR) is an important problem in machine learning, particularly when dealing with limited sample size in the target task. However, there currently lacks a method to quantify the statistical significance of the relationship between features and the response in TL-HDR settings. In this paper, we introduce a novel statistical inference framework for assessing the reliability of feature selection in TL-HDR, called PTL-SI (Post-TL Statistical Inference). The core contribution of PTL-SI is its ability to provide valid $p$-values to features selected in TL-HDR, thereby rigorously controlling the false positive rate (FPR) at desired significance level $α$ (e.g., 0.05). Furthermore, we enhance statistical power by incorporating a strategic divide-and-conquer approach into our framework. We demonstrate the validity and effectiveness of the proposed PTL-SI through extensive experiments on both synthetic and real-world high-dimensional datasets, confirming its theoretical properties and utility in testing the reliability of feature selection in TL scenarios. |
| title | Post-Transfer Learning Statistical Inference in High-Dimensional Regression |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2504.18212 |