# A Pure Hypothesis Test for Inhomogeneous Random Graph Models Based on a Kernelised Stein Discrepancy

arXiv: https://arxiv.org/abs/2505.21580 · HTML: https://mlsanity.com/paper/2505.21580/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 51 references that are in the map.
- First posted on arXiv 27 May 2025.

## Builds on (most cited first, 11 of 11)

- [A Kernel Test of Goodness of Fit](https://mlsanity.com/paper/1602.02964/) (2016)
- [Cooperative Game Theory Approaches for Network Partitioning](https://mlsanity.com/paper/1707.03587/) (2017)
- [Measuring Sample Quality with Stein's Method](https://mlsanity.com/paper/1506.03039/) (2015)
- [A goodness-of-fit test for stochastic block models](https://mlsanity.com/paper/1412.4857/) (2014)
- [A Kernel Stein Test for Comparing Latent Variable Models](https://mlsanity.com/paper/1907.00586/) (2019)
- [Online Learning of Network Bottlenecks via Minimax Paths](https://mlsanity.com/paper/2109.08467/) (2021)
- [Using Maximum Entry-Wise Deviation to Test the Goodness-of-Fit for Stochastic Block Models](https://mlsanity.com/paper/1703.06558/) (2017)
- [Monte Carlo goodness-of-fit tests for degree corrected and related stochastic blockmodels](https://mlsanity.com/paper/1612.06040/) (2016)
- [A spectral based goodness-of-fit test for stochastic block models](https://mlsanity.com/paper/2303.14508/) (2023)
- [A Mixed-Membership Model for Social Network Clustering](https://mlsanity.com/paper/1708.07604/) (2017)
- [Network Goodness-of-Fit for the block-model family](https://mlsanity.com/paper/2502.08609/) (2025)

## Built on by (most cited first, 1 of 1)

- [Nystr"om Kernel Stein Discrepancy Tests](https://mlsanity.com/paper/2605.25173/) (2026)

## Abstract (arXiv)

Complex data are often represented as a graph, which in turn can often be viewed as a realisation of a random graph, such as an inhomogeneous random graph model (IRG). For general fast goodness-of-fit tests in high dimensions, kernelised Stein discrepancy (KSD) tests are a powerful tool. Here, we develop a KSD-type test for IRG models that can be carried out with a single observation of the network. The test applies to a network of any size, but is particularly interesting for small networks for which asymptotic tests are not warranted. We also provide theoretical guarantees.