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

Wenkai Xu, Gesine Reinert
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:415-423, 2021.

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.

Cite this Paper

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. } }
Endnote
%0 Conference Paper %T A Stein Goodness-of-test for Exponential Random Graph Models %A Wenkai Xu %A Gesine Reinert %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-xu21b %I PMLR %P 415--423 %U https://proceedings.mlr.press/v130/xu21b.html %V 130 %X 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.
APA
Xu, W. & Reinert, G.. (2021). A Stein Goodness-of-test for Exponential Random Graph Models . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:415-423 Available from https://proceedings.mlr.press/v130/xu21b.html.

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