Histogram-based approach for graphon estimation via joint exploitation of multiple networks
Résumé
Exchangeable graph models represent a commonly used non-parametric approach in the modeling of network data. They are characterized by a mathematical object called a graphon. This study focuses on estimating the graphon from multiple networks generated independently from the same model, with possibly distinct sets of nodes. We propose a new histogram estimator that leverages the joint sorting of empirical degrees of the graphs. Our algorithm is extremely fast and scalable to very huge datasets. A numerical study illustrates that the proposed estimator clearly outperforms naive estimators based on the average of individual graphon estimates. Our estimator is consistent when the number of nodes per network increases.