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

Author

Listed:
  • Yiping Yang

    (Nanjing University of Finance and Economics, School of Economics)

  • Yinghui Huang

    (Chongqing Technology and Business University, School of Mathematics and Statistics)

  • Junhua Zhang

    (Beijing Information Science and Technology University, College of Mechanical and Electrical Engineering)

  • Gaorong Li

    (Beijing Normal University, School of Statistics)

Abstract

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.

Suggested Citation

  • Yiping Yang & Yinghui Huang & Junhua Zhang & Gaorong Li, 2026. "Multi-step adaptive elastic net for variable selection and classification in high-dimensional sparse logistic regression models," Computational Statistics, Springer, vol. 41(2), pages 1-38, February.
    • Handle: RePEc:spr:compst:v:41:y:2026:i:2:d:10.1007_s00180-025-01714-2
    DOI: 10.1007/s00180-025-01714-2
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    References listed on IDEAS

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    2. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
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    4. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    5. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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