A1598
Title: Multivariate inference of network moments by subsampling
Authors: Wen Zhou - New York University (United States) [presenting]
Tianxi Li - University of Minnesota (United States)
Abstract: Network moments, rescaled counts of motifs such as stars and triangles, are fundamental summaries of network structure, widely used in goodness-of-fit testing, model selection, and network comparison. While the univariate distribution of a single network moment can be approximated by subsampling, the consistency of subsampling for their joint distribution has remained unestablished. Node subsampling is proved to provide an asymptotically accurate approximation of the joint distribution of multiple network moments under a general sparse graphon model. The theoretical analysis requires a careful characterization of the dependence structure among network moments and the corresponding multivariate asymptotic convergence, going substantially beyond existing univariate results. Building on this foundation, a practically important open problem is addressed: two-sample testing between unmatchable networks with unequal edge densities. A novel subsampling-based procedure is proposed that combines sparsification with a sample-splitting strategy, yielding the first subsampling-based inferential procedure valid for this setting.
