Krylov subspace solvers for ℓ 1 regularized logistic regression method


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Output type: Journal article

UM6P affiliated Publication?: Yes

Author list: Guide M.E., Jbilou K., Koukouvinos C., Lappa A.

Publisher: Taylor & Francis: STM, Behavioural Science and Public Health Titles

Publication year: 2021

Journal: Communications in Statistics - Simulation and Computation (0361-0918)

ISSN: 0361-0918

eISSN: 1532-4141

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85104759447&doi=10.1080%2f03610918.2021.1914093&partnerID=40&md5=51d597a1fdbcb1fadd5157b6820a5ee7

Languages: English (EN-GB)


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Abstract

In this paper, we propose an approach based on Krylov subspace methods for the solution of (Formula presented.) regularized logistic regression problem. The main idea is to transform the constrained (Formula presented.) - (Formula presented.) minimization problem obtained by applying the IRLS method to a (Formula presented.) - (Formula presented.) 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 (Formula presented.) - (Formula presented.) 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 (Formula presented.) 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. © 2021 Taylor & Francis Group, LLC.


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Last updated on 2021-25-11 at 23:20