Abstract

Stein's method and Stein discrepancy have exhibited desirable properties for goodness-of-fit testing and variational inference for Euclidean data, based on the score functions for continuous probability density functions. For graph data that is discrete and embeds complex structures, alternative treatments may be required. In this talk, we will introduce Stein-based distribution measures for inference on graphs, that have been inspired by the underlying Glauber dynamics. In particular, the proposed measures are also capable of dealing with the case where only one graph sample can be observed. We start by discussing the nonparametric goodness of fit testing on exponential random graph models (ERGM), followed by model assessments on trained graph generative models which may not admit closed-form probability distributions. Moreover, we introduce SteinGen, a sample-generating scheme for graphs that produces high-quality graph samples as well as promotes sample diversity from the observation.