Uniform joint screening for ultra-high dimensional graphical models

Identifying large-scale conditional dependence structures through graphical models is a challenging yet practical problem. Under ultra-high dimensional settings, a screening procedure is generally suggested before variable selection to reduce computational costs. However, most existing screening methods examine the marginal correlations, thus not suitable to discover the conditional dependence in graphical models. To overcome this issue, we propose a new procedure called graphical uniform joint screening (GUS) for edge identification in graphical models. Instead of screening out edges nodewisely, GUS utilizes a uniform threshold for all statistics indicating the significance of different edges to adapt to various kinds of graphical structures. We demonstrate that GUS enjoys the sure screening property and even the screening consistency by preserving the rankings of the significant edges. Furthermore, a scalable implementation of GUS is developed for big data applications. Simulation and real data studies are provided to illustrate the effectiveness of the proposed method.