The Square-root Elastic Net With a New Calculating Method

The elastic net is a well-known algorithm and powerful in simultaneous estimation and variable selection under diverse conditions. In this paper, we proposed a novel version called square-root elastic net, which expands the application of the elastic net in some common cases that the noise distribution of data is not normal. We showed a calculating method based on proximal gradient descent combined with backtracking. Similar to the elastic net, the square-root elastic net can select more essential features than the sample size. Furthermore, the mean square error of the square-root elastic net is remarkably reduced when dealing with the abnormal noise compared to the elastic net.