Nonparametric graphon estimation

TL;DR

This paper introduces a nonparametric approach to network analysis using graphons, establishing consistent estimation methods applicable to both dense and sparse networks, with theoretical guarantees and practical relevance.

Contribution

It develops a general nonparametric framework for graphon estimation, including consistency proofs and rates for sparse networks, extending previous models and connecting to approximation theory.

Findings

Proves consistency of graphon estimation under broad conditions.

Provides estimation rates for sparse and dense networks.

Connects graphon estimation to approximation and nonparametric function theories.

Abstract

We propose a nonparametric framework for the analysis of networks, based on a natural limit object termed a graphon. We prove consistency of graphon estimation under general conditions, giving rates which include the important practical setting of sparse networks. Our results cover dense and sparse stochastic blockmodels with a growing number of classes, under model misspecification. We use profile likelihood methods, and connect our results to approximation theory, nonparametric function estimation, and the theory of graph limits.