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

Abstract: 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.