Study on the Properties of Penalized Logistic Regression with Adaptive Elastic Net

Logistic regression (LR) as an important data analysis method is widely used in various fields. In practical classification problem, the logistic regression always can receive a good effect. However, there are some obvious deficiencies in the traditional logistic regression model. The regularization method has been put forward. Nevertheless, some mainstream regularization logistic regression models are not good regularization methods for the lack of the Oracle property in theory. As a result, there is a certain degree of uncertainty when these methods are used. Based on this, the adaptive elastic net logistic regression (AEN-LR) is proposed. In this article we specially focus on the grouped selection property and the Oracle property of adaptive elastic net along with its model selection complexity. And the proofs of the properties are given. Through the detailed theoretical derivation, the reliable of the model can be guarantee essentially.