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Variable Selection for Sparse Logistic Regression with Grouped Variables

Author

Listed:
  • Mingrui Zhong

    (School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China)

  • Zanhua Yin

    (School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China)

  • Zhichao Wang

    (School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China)

Abstract

We present a new penalized method for estimation in sparse logistic regression models with a group structure. Group sparsity implies that we should consider the Group Lasso penalty. In contrast to penalized log-likelihood estimation, our method can be viewed as a penalized weighted score function method. Under some mild conditions, we provide non-asymptotic oracle inequalities promoting the group sparsity of predictors. A modified block coordinate descent algorithm based on a weighted score function is also employed. The net advantage of our algorithm over existing Group Lasso-type procedures is that the tuning parameter can be pre-specified. The simulations show that this algorithm is considerably faster and more stable than competing methods. Finally, we illustrate our methodology with two real data sets.

Suggested Citation

  • Mingrui Zhong & Zanhua Yin & Zhichao Wang, 2023. "Variable Selection for Sparse Logistic Regression with Grouped Variables," Mathematics, MDPI, vol. 11(24), pages 1-21, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:24:p:4979-:d:1301684
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    References listed on IDEAS

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