Differential Network Analysis via the Lasso Penalized D-Trace Loss

Biological networks often change under different environmental and genetic conditions. Understanding how these networks change becomes an important problem in biological studies. In this paper, we model the network change as the difference of two precision matrices and propose a novel loss function for estimating the precision matrix difference. Under a new irrepresentability condition, we show that the new loss function with the lasso penalty can give consistent estimates in high-dimensional setting for sub-Gaussian and polynomial-tailed distributions. An efficient algorithm is developed based on the alternating direction method to solve the optimization problem. Simulation studies and a real data analysis about colorectal cancer show that the proposed method outperforms other available methods.