Network estimation via graphon with node features

TL;DR

This paper introduces a new method for estimating network connection probabilities using graphons that incorporates node features, improving accuracy over existing methods that ignore such information.

Contribution

The paper develops a consistent graphon estimation technique that integrates node features with network data, enhancing estimation accuracy.

Findings

Incorporating node features improves graphon estimation accuracy.

The proposed method is consistent under certain conditions.

A cross-validation approach effectively selects tuning parameters.

Abstract

Estimating the probabilities of linkages in a network has gained increasing interest in recent years. One popular model for network analysis is the exchangeable graph model (ExGM) characterized by a two-dimensional function known as a graphon. Estimating an underlying graphon becomes the key of such analysis. Several nonparametric estimation methods have been proposed, and some are provably consistent. However, if certain useful features of the nodes (e.g., age and schools in social network context) are available, none of these methods was designed to incorporate this source of information to help with the estimation. This paper develops a consistent graphon estimation method that integrates the information from both the adjacency matrix itself and node features. We show that properly leveraging the features can improve the estimation. A cross-validation method is proposed to automatically select the tuning parameter of the method.