Variational Bayesian Variable Selection in Logistic Regression Based on Spike-and-Slab Lasso

Juanjuan Zhang, Weixian Wang, Mingming Yang and Maozai Tian ()
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Juanjuan Zhang: School of Digital Economy and Trade, Guangzhou Huashang College, Guangzhou 511300, China
Weixian Wang: School of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, China
Mingming Yang: School of Tourism, Xinjiang University of Finance and Economics, Urumqi 830012, China
Maozai Tian: School of Statistics and Data Science, Xinjiang University of Finance and Economics, Urumqi 830012, China

Mathematics, 2025, vol. 13, issue 13, 1-18

Abstract: Logistic regression is often used to solve classification problems. This article combines the advantages of Bayesian methods and spike-and-slab Lasso to select variables in high-dimensional logistic regression. The method of introducing a new hidden variable or approximating the lower bound is used to solve the problem of logistic functions without conjugate priors. The Laplace distribution in spike-and-slab Lasso is expressed as a hierarchical form of normal distribution and exponential distribution, so that all parameters in the model are posterior distributions that are easy to deal with. Considering the high time cost of parameter estimation and variable selection in high-dimensional models, we use the variational Bayesian algorithm to perform posterior inference on the parameters in the model. From the simulation results, it can be seen that it is an adaptive prior that can perform parameter estimation and variable selection well in high-dimensional logistic regression. From the perspective of algorithm running time, the method proposed in this article also has high computational efficiency in many cases.

Keywords: logistic regression; spike-and-slab lasso; variable selection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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