Krylov subspace solvers for regularized logistic regression method

In this paper, we propose an approach based on Krylov subspace methods for the solution of regularized logistic regression problem. The main idea is to transform the constrained - minimization problem obtained by applying the IRLS method to a - one that allow regularization matrices in the usual 2-n...

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Bibliographic Details
Published in:Communications in statistics. Simulation and computation 2023, Vol.52 (6), p.2738-2751
Main Authors: Guide, M. El, Jbilou, K., Koukouvinos, C., Lappa, A.
Format: Article
Language:English
Subjects:
Krylov subspace methods
Logistic regression model
norm
Optimization
Regression
Regression analysis
Regularization
Subspace methods
Subspaces
variable selection
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Summary:In this paper, we propose an approach based on Krylov subspace methods for the solution of regularized logistic regression problem. The main idea is to transform the constrained - minimization problem obtained by applying the IRLS method to a - one that allow regularization matrices in the usual 2-norm regularization term. The regularization parameter that controls the equilibrium between the minimization of the two terms of the - minimization problem can be then chosen inexpensively by solving some reduced minimization problems related to generalized cross-validation (GCV) methods. These reduced problems can be obtained after a few iterations of Krylov subspace based methods. The goal of our simulation study is directed toward the variable selection and the prediction accuracy performance of the proposed method in solving a regularized logistic regression problem in large dimensional data with different correlation structures among predictors. Finally, real data are used to confirm the efficiency of the proposed method in terms of the computational cost.
ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2021.1914093