The Study On The Adaptive Elastic Net Logistic Regression

Logistic Regression(LR) is regarded as an important data analysis method and which is widely used in a variety of fields. It can receive a very well result, specifically in the classification problems. However, the traditional logistic regression exist some obvious deficiencies and weakness in overcoming the complexity and over-fitting problems. For this purpose, the researchers present a lot of techniques for solving the above problems, and the regularization method was a common method, which obtained the evident effect. Nevertheless,because of the lack of the Oracle property in theory, some mainstream regularization logistic regression models are not “good” enough and these models exists some uncertainty. This paper proposed adaptive elastic net logistic regression, and the reliable of the model could be guarantee essentially result of detailing theoretical derivation. In addition, the conclusion is proven by the experiments.In this thesis, the main work includes:(1) Logistic regression model on the basis of the elastic network, the adaptive elastic network is proposed, and it can take the small and medium correlation into account among variables of model at the same time. To some extant,the prediction accuracy is improved and the variable selection capability is enhanced;furthermore, the over-fitting problem of the traditional LR model is alleviated;(2) The properties of the present model are studied, and the proofs of the properties are given;(3) In order to solve the model parameter estimation, this paper constructs the regularization algorithm based on the coordinate descent technique; what is more, a series of artificial data and real data sets were tested. The experiments indicate that the algorithm has very good capability of predict and variable selection.