A Two-Step Penalized Regression Method with Networked Predictors

Penalized regression incorporating prior dependency structure of predictors can be effective in high-dimensional data analysis (Li and Li 2008). Pan, Xie and Shen (2010) proposed a penalized regression method for better outcome prediction and variable selection by smoothing parameters over a given predictor network, which can be applied to analysis of microarray data with a given gene network. In this paper, we develop two modifications to their method for further performance enhancement. First, we employ convex programming and show its improved performance over an approximate optimization algorithm implemented in their original proposal. Second, we perform bias reduction after initial variable selection through a new penalty, leading to better parameter estimates and outcome prediction. Simulations have demonstrated substantial performance improvement of the proposed modifications over the original method.