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<p>In high-dimensional data analysis, particularly when handling highly correlated covariates, the challenge of simultaneous variable selection and classification remains prevalent in machine learning. To tackle this issue, we propose multi-step adaptive Elastic Net (MSA-Enet) for logistic regression models, which integrates a multi-step estimation framework with an adaptive penalty structure. MSA-Enet enhances the selection of relevant variables through a strategy of applying small repeated penalties and improves classification prediction accuracy. Theoretically, the proposed method is shown to select the true model with high probability and achieve an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_2\)</EquationSource> </InlineEquation>-norm error bound under some regularity conditions. Finally, through simulation studies and the analysis of two gene expression datasets, MSA-Enet reduces model complexity without compromising the accuracy of classification predictions.</p>

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Multi-step adaptive elastic net for variable selection and classification in high-dimensional sparse logistic regression models

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Yiping Yang,
  • Yinghui Huang,
  • Junhua Zhang,
  • Gaorong Li

摘要

In high-dimensional data analysis, particularly when handling highly correlated covariates, the challenge of simultaneous variable selection and classification remains prevalent in machine learning. To tackle this issue, we propose multi-step adaptive Elastic Net (MSA-Enet) for logistic regression models, which integrates a multi-step estimation framework with an adaptive penalty structure. MSA-Enet enhances the selection of relevant variables through a strategy of applying small repeated penalties and improves classification prediction accuracy. Theoretically, the proposed method is shown to select the true model with high probability and achieve an \(L_2\) -norm error bound under some regularity conditions. Finally, through simulation studies and the analysis of two gene expression datasets, MSA-Enet reduces model complexity without compromising the accuracy of classification predictions.