SIMPLE-RC: Group network inference with NonSharp nulls and weak signals

原文摘要

Large-scale network inference with uncertainty quantification has important applications in natural, social and medical sciences. The recent work of Fan et al. (J. R. Stat. Soc. Ser. B. Stat. Methodol. 84 (2022) 630–653) introduced a general framework of statistical inference on membership profiles in large networks (SIMPLE) for testing the sharp null hypothesis that a pair of given nodes share the same membership profile. In real applications, there are often groups of nodes under investigation that may share similar membership profiles in the presence of relatively weaker signals than the setting considered in SIMPLE. To address these practical challenges, in this paper, we propose a SIMPLE method with random coupling (SIMPLE-RC) for testing the nonsharp composite null hypothesis that a group of given nodes shares similar (not necessarily identical) membership profiles under weaker signals. Utilizing the idea of random coupling, we construct our test as the maximum of the SIMPLE tests for subsampled node pairs from the group. Such a technique significantly reduces the correlation among individual SIMPLE tests while largely maintaining the power, enabling delicate analysis of the asymptotic distributions of the SIMPLE-RC test. Our method and theory cover both the cases with and without node degree heterogeneity. These new theoretical developments are empowered by a second-order expansion of spiked eigenvectors under the ℓ∞-norm, built upon our work for random matrices with weak spikes. Our theoretical results and the practical advantages of the newly proposed method are demonstrated through simulations and real data examples.

摘要来源：Crossref