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

2025-05-27

AI Summary

Existing goodness-of-fit tests are inapplicable to inhomogeneous random graph (IRG) models—characterized by high-dimensional, complex graph structures—when only a single observed graph is available. Method: We propose the first kernelized Stein discrepancy (KSD) one-sample test tailored for IRGs: it requires no asymptotic distributional assumptions, is independent of network size, and accommodates graphs of arbitrary scale. Crucially, we systematically extend the KSD framework to IRG modeling and testing by designing graph-adapted function spaces and kernels, enabling nonparametric, non-asymptotic, and size-invariant inference. Results: We establish theoretical consistency and optimal convergence rates for the test. Empirical evaluations demonstrate strong finite-sample statistical power alongside strict control of Type-I error.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Kernel Methods
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Assessing fit of inhomogeneous random graph models
• Developing KSD test for single network observation
• Providing theoretical guarantees for the test

Innovation

• Kernelised Stein Discrepancy for IRG models
• Single network observation goodness-of-fit test
• Theoretical guarantees for any network size