Post-Transfer Learning Statistical Inference in High-Dimensional Regression
This addresses the lack of reliable statistical inference methods for researchers and practitioners using transfer learning in high-dimensional regression, offering a novel framework for rigorous feature selection testing.
The paper tackles the problem of quantifying statistical significance in feature selection for high-dimensional regression with transfer learning, introducing PTL-SI to provide valid p-values that control false positive rates at desired levels like 0.05.
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.