Low-Rank Graphon Learning for Networks

Xinyuan Fan, Feiyan Ma, Chenlei Leng, Weichi Wu

Keywords: low-rank graphon, subgraph counts, connection probability matrix, nonparametric statistics, network analysis

Abstract: Graphons offer a powerful framework for modeling large-scale networks, yet estimation remains challenging. We propose a novel approach that leverages a low-rank additive representation, yielding both a low-rank connection probability matrix and a low-rank graphon--two goals rarely achieved jointly. Our method resolves identification issues and enables an efficient sequential algorithm based on subgraph counts and interpolation. We establish consistency and demonstrate strong empirical performance in terms of computational efficiency and estimation accuracy through simulations and data analysis.

Primary Area: Probabilistic methods (e.g., variational inference, causal inference, Gaussian processes)

Submission Number: 17745