Low-Rank Graphon Learning for Networks

TL;DR

This paper introduces a low-rank additive approach for estimating graphons, improving efficiency and accuracy in modeling large networks.

Contribution

It presents a novel low-rank representation method that jointly estimates a connection probability matrix and a graphon, addressing identification and computational challenges.

Findings

Method achieves consistent estimation of low-rank graphons.

Demonstrates superior computational efficiency in simulations.

Shows strong empirical performance in real data 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.