Structure learning of exponential family graphical model with false discovery rate control

Probabilistic graphical models enjoy great popularity in a wide range of domains due to their ability to model the conditional dependency relationships among random variables. This paper explores the structure learning for the exponential family graphical model with false discovery rate (FDR) control. Most existing FDR-controlled structure learning procedures have been designed for the Gaussian graphical model (GGM). A systematic approach for more general exponential family graphical models is still lacking. In this paper, we introduce a unified procedure to learn the structure of the exponential family graphical model with FDR control utilizing the symmetrized data aggregation (SDA) technique via sample splitting, data screening, and information pooling. We show that our method controls FDR asymptotically under some mild conditions. Extensive simulation results and two real-data examples validate the effectiveness of our method.