Uniform knockoff filter for high-dimensional controlled graph recovery

Reproducible learning of high-dimensional graphical structures is fundamentally important in numerous contemporary applications, as it visually reveals the underlying conditional dependencies among complex network data. In this paper, we introduce a novel procedure called the uniform graphical knockoff filter, which controls the overall false discovery rate (FDR) in Gaussian graph recovery by utilizing knockoff variables and a uniform threshold. Compared to existing methods, it is more robust to varying levels of sparsity in the true graph. We provide theoretical justifications for the procedure, demonstrating that the FDR can be asymptotically controlled and that the power is asymptotically one under mild conditions. Extensive numerical studies confirm the robust and competitive finite-sample performance of the proposed method.