Recovering the Graphical Structures via Knockoffs

Learning the dependence structures in Gaussian graphical models is of fundamental importance in many contemporary applications. Despite the fast growing literature, procedures with guaranteed FDR control for recovering the graphical structures are rare. In this paper, we propose a new procedure based on constructing knockoff variables such that the FDR for graph recovery can be controlled nodewisely. The suggested method combines the strengths of FDR control via knockoffs in linear regression settings and neighborhood selection which converts the problem of identifying Gaussian graphical structures into nodewise variable selection. Numerical studies show that the proposed procedure enjoys better statistical power compared with existing methods.