AISTATS 2021poster17 citations

A Stein Goodness-of-test for Exponential Random Graph Models

Wenkai Xu, Gesine Reinert

Abstract

We propose and analyse a novel nonparametric goodness-of-fit testing procedure for ex-changeable exponential random graph model (ERGM) 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 of kernel Stein discrepancy, a divergence constructed via Stein’s method using functions from a reproducing kernel Hilbert space (RKHS), combined with a discrete Stein operator for ERGMs. The test is a Monte Carlo test using simulated networks from the target ERGM. We show theoretical properties for the testing procedure w.r.t a class of ERGMs. Simulation studies and real network applications are presented.

BibTeX
@InProceedings{pmlr-v130-xu21b,
  title = 	 { A Stein Goodness-of-test for Exponential Random Graph Models },
  author =       {Xu, Wenkai and Reinert, Gesine},
  booktitle = 	 {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics},
  pages = 	 {415--423},
  year = 	 {2021},
  editor = 	 {Banerjee, Arindam and Fukumizu, Kenji},
  volume = 	 {130},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {13--15 Apr},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v130/xu21b/xu21b.pdf},
  url = 	 {https://proceedings.mlr.press/v130/xu21b.html},
  abstract = 	 { We propose and analyse a novel nonparametric goodness-of-fit testing procedure for ex-changeable exponential random graph model (ERGM) 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 of kernel Stein discrepancy, a divergence constructed via Stein’s method using functions from a reproducing kernel Hilbert space (RKHS), combined with a discrete Stein operator for ERGMs. The test is a Monte Carlo test using simulated networks from the target ERGM. We show theoretical properties for the testing procedure w.r.t a class of ERGMs. Simulation studies and real network applications are presented. }
}
A Stein Goodness-of-test for Exponential Random Graph Models · AISTATS 2021