# A Stein Goodness of fit Test for Exponential Random Graph Models

arXiv: https://arxiv.org/abs/2103.00580 · HTML: https://mlsanity.com/paper/2103.00580/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 74 references that are in the map.
- First posted on arXiv 28 Feb 2021.

## Builds on (most cited first, 23 of 23)

- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation](https://mlsanity.com/paper/1602.03253/) (2016)
- [A Survey on Graph Kernels](https://mlsanity.com/paper/1903.11835/) (2019)
- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [Minimum Stein Discrepancy Estimators](https://mlsanity.com/paper/1906.08283/) (2019)
- [On Valid Optimal Assignment Kernels and Applications to Graph Classification](https://mlsanity.com/paper/1606.01141/) (2016)
- [A Linear-Time Kernel Goodness-of-Fit Test](https://mlsanity.com/paper/1705.07673/) (2017)
- [Stochastic Stein Discrepancies](https://mlsanity.com/paper/2007.02857/) (2020)
- [A Wild Bootstrap for Degenerate Kernel Tests](https://mlsanity.com/paper/1408.5404/) (2014)
- [Testing Goodness of Fit of Conditional Density Models with Kernels](https://mlsanity.com/paper/2002.10271/) (2020)
- [A Kernel Stein Test for Comparing Latent Variable Models](https://mlsanity.com/paper/1907.00586/) (2019)
- [An Adaptive Test of Independence with Analytic Kernel Embeddings](https://mlsanity.com/paper/1610.04782/) (2016)
- [A Stein Goodness-of-fit Test for Directional Distributions](https://mlsanity.com/paper/2002.06843/) (2020)
- [Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Data](https://mlsanity.com/paper/2008.08397/) (2020)
- [Informative Features for Model Comparison](https://mlsanity.com/paper/1810.11630/) (2018)
- [Subsampling bootstrap of count features of networks](https://mlsanity.com/paper/1312.2645/) (2013)
- [Exponential random graphs behave like mixtures of stochastic block models](https://mlsanity.com/paper/1707.01227/) (2017)
- [Optimal Single Sample Tests for Structured versus Unstructured Network Data](https://mlsanity.com/paper/1802.06186/) (2018)
- [A Bootstrap Method for Goodness of Fit and Model Selection with a Single Observed Network](https://mlsanity.com/paper/1806.11220/) (2018)
- [Spectral goodness of fit for network models](https://mlsanity.com/paper/1407.7247/) (2014)
- [Selection of Exponential-Family Random Graph Models via Held-Out Predictive Evaluation (HOPE)](https://mlsanity.com/paper/1908.05873/) (2019)

## Built on by (most cited first, 2 of 2)

- [Composite Goodness-of-fit Tests with Kernels](https://mlsanity.com/paper/2111.10275/) (2021)
- [Spectral goodness-of-fit tests for complete and partial network data](https://mlsanity.com/paper/2106.09702/) (2021)

## Abstract (arXiv)

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.