A Stein Goodness of fit Test for Exponential Random Graph Models
Methodology
2021-03-02 v1 Machine Learning
Abstract
We propose and analyse a novel nonparametric goodness of fit testing procedure for exchangeable exponential random graph models (ERGMs) when a single network realisation is observed. The test determines how likely it is that the observation is generated from a target unnormalised ERGM density. Our test statistics are derived from a kernel Stein discrepancy, a divergence constructed via Steins method using functions in a reproducing kernel Hilbert space, combined with a discrete Stein operator for ERGMs. The test is a Monte Carlo test based on simulated networks from the target ERGM. We show theoretical properties for the testing procedure for a class of ERGMs. Simulation studies and real network applications are presented.
Cite
@article{arxiv.2103.00580,
title = {A Stein Goodness of fit Test for Exponential Random Graph Models},
author = {Wenkai Xu and Gesine Reinert},
journal= {arXiv preprint arXiv:2103.00580},
year = {2021}
}