Regularized logistic regression with the Atan in high dimensional data

Abstract

Logistic regression models play an important role in analyzing binary classification problems in medical and biological data. One common method for estimating the parameters of a logistic regression model is the maximum likelihood method. However, this method does not perform well in high-dimensional settings or in the presence of multicollinearity. To overcome these problems, a penalty term is added to the objective function. In this paper, we propose a method for parameter estimation and variable selection in logistic regression models using an L0 -like arctangent (Atan) regularization approach. The Atan penalty, which is based on the arctangent function, enjoys oracle properties. The performance of the regularized logistic regression model with the Atan penalty is compared with that of the fused lasso and the SELO penalty. Monte Carlo simulation studies are conducted under different sample sizes and different standard deviation settings. In addition, a real data set is used to evaluate the performance of the proposed method. The results show that the proposed estimator outperforms the competing methods (fused lasso and SELO) in terms of both estimation accuracy and variable selection.