Multivariate Inference of Network Moments by Subsampling

In this paper, we study the characterization of a network population by analyzing a single observed network, focusing on the counts of multiple network motifs or their corresponding multivariate network moments. We introduce an algorithm based on node subsampling to approximate the nontrivial joint distribution of the network moments, and prove its asymptotic accuracy. By examining the joint distribution of these moments, our approach captures complex dependencies among network motifs, making a significant advancement over earlier methods that rely on individual motifs marginally. This enables more accurate and robust network inference. Through real-world applications, such as comparing coexpression networks of distinct gene sets and analyzing collaboration patterns within the statistical community, we demonstrate that the multivariate inference of network moments provides deeper insights than marginal approaches, thereby enhancing our understanding of network mechanisms.