Stochastic blockmodel approximation of a graphon: Theory and consistent estimation

TL;DR

This paper introduces a computationally efficient method to estimate a graphon from observed networks using a stochastic blockmodel approximation, ensuring consistent estimation as network size grows.

Contribution

It proposes a novel SBA-based procedure for graphon estimation that is both computationally feasible and statistically consistent.

Findings

The SBA method provides consistent graphon estimates for large networks.

Estimation error diminishes as network size increases.

The approach is applicable to exchangeable graph models.

Abstract

Non-parametric approaches for analyzing network data based on exchangeable graph models (ExGM) have recently gained interest. The key object that defines an ExGM is often referred to as a graphon. This non-parametric perspective on network modeling poses challenging questions on how to make inference on the graphon underlying observed network data. In this paper, we propose a computationally efficient procedure to estimate a graphon from a set of observed networks generated from it. This procedure is based on a stochastic blockmodel approximation (SBA) of the graphon. We show that, by approximating the graphon with a stochastic block model, the graphon can be consistently estimated, that is, the estimation error vanishes as the size of the graph approaches infinity.