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<p>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 <i>PTL-SI</i> (<Emphasis Type="Underline">P</Emphasis>ost-<Emphasis Type="Underline">TL</Emphasis> <Emphasis Type="Underline">S</Emphasis>tatistical <Emphasis Type="Underline">I</Emphasis>nference). The core contribution of PTL-SI is its ability to provide valid <i>p</i>-values to features selected in TL-HDR, thereby rigorously controlling the false positive rate (FPR) at desired significance level <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11222_2025_10738_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> (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.</p>

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Post-transfer learning statistical inference in high-dimensional regression

  • 期刊论文

  • 发表日期：

    2025年9月29日

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  • Nguyen Vu Khai Tam,
  • Cao Huyen My,
  • Vo Nguyen Le Duy

摘要

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 \(\alpha \) 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.