<p>Feature selection is a fundamental challenge in high-dimensional regression, where identifying the most relevant variables is essential for both interpretability and predictive performance. Although LASSO is widely used for this purpose, its reliance on a single tuning parameter <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation> often limits its ability to recover the true active set. We address this issue by introducing a feature importance score, denoted <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(I^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>I</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>, that leverages the full LASSO path and aggregates information across multiple regularization levels. We develop two complementary algorithms for computing and applying this score: LASSO.PATH, which efficiently constructs <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(I^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>I</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation>, and LASSO.PATH.BISEC, which selects variables by estimating an optimal data-driven threshold. We also propose the score-plot, a graphical tool that clearly separates relevant from irrelevant variables facilitating a more intuitive selection process. Through simulations and real data analyses, we demonstrate that our approach improves feature selection accuracy and reduces false discoveries compared with traditional LASSO-based methods.</p>

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The LASSO path as a feature importance proxy

  • Lucas Fernández-Piana,
  • Verónica Moreno

摘要

Feature selection is a fundamental challenge in high-dimensional regression, where identifying the most relevant variables is essential for both interpretability and predictive performance. Although LASSO is widely used for this purpose, its reliance on a single tuning parameter \(\lambda \) λ often limits its ability to recover the true active set. We address this issue by introducing a feature importance score, denoted \(I^*\) I , that leverages the full LASSO path and aggregates information across multiple regularization levels. We develop two complementary algorithms for computing and applying this score: LASSO.PATH, which efficiently constructs \(I^*\) I , and LASSO.PATH.BISEC, which selects variables by estimating an optimal data-driven threshold. We also propose the score-plot, a graphical tool that clearly separates relevant from irrelevant variables facilitating a more intuitive selection process. Through simulations and real data analyses, we demonstrate that our approach improves feature selection accuracy and reduces false discoveries compared with traditional LASSO-based methods.