Reproducible learning in large-scale graphical models

Abstract

Learning the conditional dependence structures through high-dimensional graphical models is of fundamental importance in many contemporary applications. Despite the fast growing literature on graphical models, a practical issue of reproducibility remains largely unexplored as most of existing methods for graph recovery do not guarantee the false discovery rate (FDR) control. In this paper, we propose a new procedure, called the high-dimensional graphical knockoff filter, to control the overall FDR for large-scale graph recovery. The proposed procedure enjoys not only theoretical guarantees and high power but also the robustness of FDR control even when the population precision matrices of predictors are replaced by consistent estimates. Furthermore, a scalable implementation approach is developed such that all knockoff variables can be generated through one single estimation of the overall graphical structure. Our new methodology and results are evidenced by numerical studies.