Group Logistic Regression Models with l p,q Regularization

Yanfang Zhang, Chuanhua Wei and Xiaolin Liu
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Yanfang Zhang: College of Science, Minzu University of China, 27 Zhongguancun South Street, Haidian District, Beijing 100081, China
Chuanhua Wei: College of Science, Minzu University of China, 27 Zhongguancun South Street, Haidian District, Beijing 100081, China
Xiaolin Liu: College of Science, Minzu University of China, 27 Zhongguancun South Street, Haidian District, Beijing 100081, China

Mathematics, 2022, vol. 10, issue 13, 1-15

Abstract: In this paper, we proposed a logistic regression model with l p , q regularization that could give a group sparse solution. The model could be applied to variable-selection problems with sparse group structures. In the context of big data, the solutions for practical problems are often group sparse, so it is necessary to study this kind of model. We defined the model from three perspectives: theoretical, algorithmic and numeric. From the theoretical perspective, by introducing the notion of the group restricted eigenvalue condition, we gave the oracle inequality, which was an important property for the variable-selection problems. The global recovery bound was also established for the logistic regression model with l p , q regularization. From the algorithmic perspective, we applied the well-known alternating direction method of multipliers (ADMM) algorithm to solve the model. The subproblems for the ADMM algorithm were solved effectively. From the numerical perspective, we performed experiments for simulated data and real data in the factor stock selection. We employed the ADMM algorithm that we presented in the paper to solve the model. The numerical results were also presented. We found that the model was effective in terms of variable selection and prediction.

Keywords: logistic regression; group sparse; oracle inequality; l p,q regularization; ADMM algorithm; multi-factors stock selection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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