The cluster D-trace loss for differential network analysis.

A growing literature suggests that gene expression can be greatly altered in disease conditions, and identifying those changes will improve the understanding of complex diseases such as cancers or diabetes. A prevailing direction in the analysis of gene expression studies the changes in gene pathways which include sets of related genes. Therefore, introducing structured exploration to differential analysis of gene expression networks may lead to meaningful discoveries. The topic of this paper is differential network analysis, which focuses on capturing the differences between two or more precision matrices. We discuss the connection between the thresholding method and the D-trace loss method on differential network analysis in the case that the precision matrices share the common connected components. Based on this connection, we further propose the cluster D-trace loss method which directly estimates the differential network and achieves model selection consistency. Simulation studies demonstrate its improved performance and computational efficiency. Finally, the usefulness of our proposed estimator is demonstrated by a real-data analysis on non-small cell lung cancer.