为迁移学习中的高维回归提供可验证的特征显著性检验方法。
Post-Transfer Learning Statistical Inference in High-Dimensional Regression
- 基于分治策略构建后迁移学习统计推断框架
- 在α=0.05下严格控制假阳性率，支持可靠特征选择
- 适用于小样本高维场景，适合需要可解释性的研究者
迁移学习（TL）在高维回归（HDR）中具有重要意义，尤其在目标任务样本量有限时。然而，当前尚无方法量化特征与响应变量之间关系的统计显著性。本文提出一种新的统计推断框架PTL-SI（Post-TL Statistical Inference），用于评估TL-HDR中特征选择的可靠性。其核心贡献是为TL-HDR中选出的特征提供有效的$ p $-值，从而在设定显著性水平α（如0.05）下严格控制假阳性率（FPR）。此外，通过引入分治策略提升统计功效。我们在合成数据和真实高维数据集上进行了大量实验，验证了PTL-SI的有效性与理论性质，证实其在测试迁移学习中特征选择可靠性方面的实用性。
原文摘要 · Abstract (English)
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.
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