Variable Selection for Sparse Logistic Regression with Grouped Variables

Mingrui Zhong, Zanhua Yin () and Zhichao Wang
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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

Mathematics, 2023, vol. 11, issue 24, 1-21

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.

Keywords: high-dimensional data; non-asymptotic inequality; logistic regression; variable selection; block coordinate descent algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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