On RKHS Choices for Assessing Graph Generators via Kernel Stein Statistics
This work addresses the practical challenge of kernel selection for statistical tests on graph models, which is incremental but important for researchers and practitioners in network analysis.
The paper investigates how the choice of reproducing kernel Hilbert space (RKHS) kernels affects the performance of kernel Stein discrepancy tests for assessing graph generators, finding that kernel selection impacts test power and computational runtime in both dense and sparse graph regimes.
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.