Local linear graphon estimation using covariates

• 成果类型: Article
• 署名作者: Chandna, S.; Olhede, S. C.; Wolfe, P. J.
• 署名单位: University of London; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Purdue University System; Purdue University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asab057
• 发表日期: 2022
• 页码: 721734
• 关键词: network; models

摘要

We consider local linear estimation of the graphon function, which determines probabilities of pairwise edges between nodes in an unlabelled network. Real-world networks are typically characterized by node heterogeneity, with different nodes exhibiting different degrees of interaction. Existing approaches to graphon estimation are limited to local constant approximations, and are not designed to estimate heterogeneity across the full network. In this paper, we show how continuous node covariates can be employed to estimate heterogeneity in the network via a local linear graphon estimator. We derive the bias and variance of an oracle-based local linear graphon estimator, and thus obtain the mean integrated squared error optimal bandwidth rule. We also provide a plug-in bandwidth selection procedure that makes local linear estimation for unlabelled networks practically feasible. The finite-sample performance of our approach is investigated in a simulation study, and the method is applied to a school friendship network and an email network to illustrate its advantages over existing methods.