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December 2019 Sampling and estimation for (sparse) exchangeable graphs
Victor Veitch, Daniel M. Roy
Ann. Statist. 47(6): 3274-3299 (December 2019). DOI: 10.1214/18-AOS1778

Abstract

Sparse exchangeable graphs on $\mathbb{R}_{+}$, and the associated graphex framework for sparse graphs, generalize exchangeable graphs on $\mathbb{N}$, and the associated graphon framework for dense graphs. We develop the graphex framework as a tool for statistical network analysis by identifying the sampling scheme that is naturally associated with the models of the framework, formalizing two natural notions of consistent estimation of the parameter (the graphex) underlying these models, and identifying general consistent estimators in each case. The sampling scheme is a modification of independent vertex sampling that throws away vertices that are isolated in the sampled subgraph. The estimators are variants of the empirical graphon estimator, which is known to be a consistent estimator for the distribution of dense exchangeable graphs; both can be understood as graph analogues to the empirical distribution in the i.i.d. sequence setting. Our results may be viewed as a generalization of consistent estimation via the empirical graphon from the dense graph regime to also include sparse graphs.

Citation

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Victor Veitch. Daniel M. Roy. "Sampling and estimation for (sparse) exchangeable graphs." Ann. Statist. 47 (6) 3274 - 3299, December 2019. https://doi.org/10.1214/18-AOS1778

Information

Received: 1 August 2017; Revised: 1 October 2018; Published: December 2019
First available in Project Euclid: 31 October 2019

Digital Object Identifier: 10.1214/18-AOS1778

Subjects:
Primary: 62G05
Secondary: 62D05, 62G09, 62M99

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 6 • December 2019
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