IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v41y2026i2d10.1007_s00180-025-01714-2.html

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-025-01714-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-025-01714-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    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).
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    2. Peter Bühlmann & Jacopo Mandozzi, 2014. "High-dimensional variable screening and bias in subsequent inference, with an empirical comparison," Computational Statistics, Springer, vol. 29(3), pages 407-430, June.
    3. Capanu, Marinela & Giurcanu, Mihai & Begg, Colin B. & Gönen, Mithat, 2023. "Subsampling based variable selection for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    4. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    5. Zeyu Bian & Erica E. M. Moodie & Susan M. Shortreed & Sahir Bhatnagar, 2023. "Variable selection in regression‐based estimation of dynamic treatment regimes," Biometrics, The International Biometric Society, vol. 79(2), pages 988-999, June.
    6. Christidis, Anthony-Alexander & Van Aelst, Stefan & Zamar, Ruben, 2025. "Multi-model subset selection," Computational Statistics & Data Analysis, Elsevier, vol. 203(C).
    7. Edwin Kipruto & Willi Sauerbrei, 2025. "Unraveling Similarities and Differences Between Non-Negative Garrote and Adaptive Lasso: A Simulation Study in Low- and High-Dimensional Data," Stats, MDPI, vol. 8(3), pages 1-33, August.
    8. Zanhua Yin, 2020. "Variable selection for sparse logistic regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 821-836, October.
    9. Dumitrescu, Elena & Hué, Sullivan & Hurlin, Christophe & Tokpavi, Sessi, 2022. "Machine learning for credit scoring: Improving logistic regression with non-linear decision-tree effects," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1178-1192.
    10. Pei Wang & Shunjie Chen & Sijia Yang, 2022. "Recent Advances on Penalized Regression Models for Biological Data," Mathematics, MDPI, vol. 10(19), pages 1-24, October.
    11. Zakariya Yahya Algamal & Muhammad Hisyam Lee, 2019. "A two-stage sparse logistic regression for optimal gene selection in high-dimensional microarray data classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 753-771, September.
    12. Dai, Linlin & Chen, Kani & Sun, Zhihua & Liu, Zhenqiu & Li, Gang, 2018. "Broken adaptive ridge regression and its asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 334-351.
    13. Posch, Konstantin & Arbeiter, Maximilian & Pilz, Juergen, 2020. "A novel Bayesian approach for variable selection in linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    14. Tanin Sirimongkolkasem & Reza Drikvandi, 2019. "On Regularisation Methods for Analysis of High Dimensional Data," Annals of Data Science, Springer, vol. 6(4), pages 737-763, December.
    15. Fang, Xiaolei & Paynabar, Kamran & Gebraeel, Nagi, 2017. "Multistream sensor fusion-based prognostics model for systems with single failure modes," Reliability Engineering and System Safety, Elsevier, vol. 159(C), pages 322-331.
    16. Hui Xiao & Yiguo Sun, 2019. "On Tuning Parameter Selection in Model Selection and Model Averaging: A Monte Carlo Study," JRFM, MDPI, vol. 12(3), pages 1-16, June.
    17. Daniel, Jeffrey & Horrocks, Julie & Umphrey, Gary J., 2018. "Penalized composite likelihoods for inhomogeneous Gibbs point process models," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 104-116.
    18. van Erp, Sara & Oberski, Daniel L. & Mulder, Joris, 2018. "Shrinkage priors for Bayesian penalized regression," OSF Preprints cg8fq, Center for Open Science.
    19. T. Tony Cai & Zijian Guo & Yin Xia, 2023. "Statistical inference and large-scale multiple testing for high-dimensional regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(4), pages 1135-1171, December.
    20. Hirose, Kei & Tateishi, Shohei & Konishi, Sadanori, 2013. "Tuning parameter selection in sparse regression modeling," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 28-40.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:41:y:2026:i:2:d:10.1007_s00180-025-01714-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.