High‐dimensional differential networks with sparsity and reduced‐rank

Differential network analysis plays a crucial role in capturing nuanced changes in conditional correlations between two samples. Under the high‐dimensional setting, the differential network, that is, the difference between the two precision matrices are usually stylized with sparse signals and some low‐rank latent factors. Recognizing the distinctions inherent in the precision matrices of such networks, we introduce a novel approach, termed ‘SR‐Network’ for the estimation of sparse and reduced‐rank differential networks. This method directly assesses the differential network by formulating a convex empirical loss function with ‐norm and nuclear norm penalties. The study establishes finite‐sample error bounds for parameter estimation and highlights the superior performance of the proposed method through extensive simulations and real data studies. This research significantly contributes to the advancement of methodologies for accurate analysis of differential networks, particularly in the context of structures characterized by sparsity and low‐rank features.