Gene regulation network inference with joint sparse Gaussian graphical models

Revealing biological networks is one key objective in systems biology. With microarrays, researchers now routinely measure expression profiles at the genome level under various conditions, and, such data may be utilized to statistically infer gene regulation networks. Gaussian graphical models (GGMs) have proven useful for this purpose by modeling the Markovian dependence among genes. However, a single GGM may not be adequate to describe the potentially differing networks across various conditions, and hence it is more natural to infer multiple GGMs from such data. In the present study, we propose a class of nonconvex penalty functions aiming at the estimation of multiple GGMs with a flexible <i>joint sparsity</i> constraint. We illustrate the property of our proposed nonconvex penalty functions by simulation study. We then apply the method to a gene expression data set from the GenCord Project, and show that our method can identify prominent pathways across different conditions.