A Comparison of Two-Stage Approaches Based on Penalized Regression for Estimating Gene Networks

Graphical models are commonly used for illustrating gene networks. However, estimating directed networks are generally challenging because of the limited sample size compared with the dimensionality of an experiment. Many previous studies have provided insight into the problem, and recently, two-stage approaches have shown significant improvements for estimating directed acyclic graphs. These two-stage approaches find neighborhoods in the first stage and determine the directions of the edges in the second stage. However, although numerous methods to find neighborhoods and determine directions exist, the most appropriate method to use with two-stage approaches has not been evaluated. Therefore, we compared such methods through extensive simulations to select effective methods for the first and second stages. Results show that adaptive lasso is the most effective for both stages in most cases. In addition, we compared methods to handle asymmetric entries to estimate an undirected network. Some previous studies indicate that the method used to handle asymmetric entries does not affect performance significantly; however, we found that the selection of the handling method for such edges is a significant factor for finding neighborhoods when using adaptive lasso.