Network inference from contrastive groups using discriminative structural regularization

Gaussian graphical models (GGMs) are a popular tool for exploring conditional dependence among high dimensional data. We consider developing an estimator for GGMs for multiple graph analysis, wherein the graphs are assumed to come from two (or more) contrastive groups, and exhibit not only major global similarity, but also substantial betweengroup disparity. Under this setting, inferring each group of networks separately ignores the common structure, while simply assuming a global common network structure would mask the critical disparity. We propose a novel approach to pursue simultaneous network inference using discriminative and adaptive structural regularizations. We introduce a heterogeneity ratio parameter to balance the within group similarity and the between group disparity. This formulation for the first time, to our knowledge, generalizes the existing single-group network analysis to multiple-group network analysis. In other words, our proposed multiple-group network analysis reduces to single-group network analysis, when the heterogeneity ratio equal to 1. By iteratively updating a global regularization template with individual network structures, together with a feature screening module specifying relevant dimensions to satisfy the group-level constraints, our generalized approach can recover the underlying conditional independence with greater exibility and improved accuracy. Theoretically, we show the asymptotic consistency for the proposed method in joint reconstruction of multiple network structures. We demonstrate its superior performance via extensive simulation studies. We also illustrate its practical usage in an application to polychromatic ow cytometry data sets for protein interactions under different conditions.