On RKHS Choices for Assessing Graph Generators via Kernel Stein Statistics

TL;DR

This paper evaluates how the choice of RKHS affects the performance of kernel Stein discrepancy tests for assessing graph generator models, focusing on both synthetic and real-world networks.

Contribution

It provides an analysis of RKHS selection impact on KSD test power and runtime for graph models, extending previous work to diverse graph regimes.

Findings

RKHS choice significantly influences test power and computational efficiency.

Different kernels perform variably across dense and sparse graph regimes.

Experimental results highlight optimal kernel choices for specific network types.

Abstract

Score-based kernelised Stein discrepancy (KSD) tests have emerged as a powerful tool for the goodness of fit tests, especially in high dimensions; however, the test performance may depend on the choice of kernels in an underlying reproducing kernel Hilbert space (RKHS). Here we assess the effect of RKHS choice for KSD tests of random networks models, developed for exponential random graph models (ERGMs) in Xu and Reinert (2021)and for synthetic graph generators in Xu and Reinert (2022). We investigate the power performance and the computational runtime of the test in different scenarios, including both dense and sparse graph regimes. Experimental results on kernel performance for model assessment tasks are shown and discussed on synthetic and real-world network applications.