A Kernelised Stein Discrepancy for Assessing the Fit of Inhomogeneous Random Graph Models

Complex data are often represented as a graph, which in turn can often be viewed as a realisation of a random graph, such as of 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, test, and analyse a KSD-type goodness-of-fit test for IRG models that can be carried out with a single observation of the network. The test is applicable to a network of any size and does not depend on the asymptotic distribution of the test statistic. We also provide theoretical guarantees.

@article{fatima2025_2505.21580,
  title={ A Kernelised Stein Discrepancy for Assessing the Fit of Inhomogeneous Random Graph Models },
  author={ Anum Fatima and Gesine Reinert },
  journal={arXiv preprint arXiv:2505.21580},
  year={ 2025 }
}