Selection of regularization model for linear regression under high-dimensional data

The data collected in current practical applications in various fields is gradually developing towards the direction of ultra-high-dimensional and large-scale, and a considerable portion of traditional analysis methods significantly reduce the processing efficiency of high-dimensional data. Therefore, it is essential to establish methods that focus on processing high dimensional data. In this paper, the Elastic-net model is selected as the basic regularization model for processing high-dimensional sparse data, and a penalty factor is added to enhance its ability to retain key features. To reduce the computational burden brought by high-dimensional data, we propose applying the "two-step" procedure of SSR+PCD screening rule and fitting method to the model containing penalty factors. In terms of the selection of tuning parameters, the traditional Cross-validation is replaced by Information Criterion, and the application of Information Criterion is extended to the regularization model with screening rules, so as to broaden the application range of Information Criterion. Through data simulation studies, we confirm the rationality of penalty factor addition and the ability of the selected Information Criterion to choose tuning parameters under this model, and an example is given to illustrate its application in processing high-dimensional gene expression data.