Wepropose and analyse anovel statistical procedure, coinedAgraSSt,to assess the quality of graph generators which may not be available in explicit forms. In particular, AgraSSt can be used to determine whether alearned graph generating process iscapable ofgenerating graphs which resemble agiveninput graph.

Stein discrepancies (SDs) monitor convergence andnon-convergence inapprox-imate inference when exact integration and sampling are intractable. However,the computation of a Stein discrepancy can be prohibitive if the Stein operator - often a sum over likelihood terms or potentials - is expensive to evaluate.

Stein discrepancies (SDs) monitor convergence and non-convergence in approximate inference when exact integration and sampling are intractable. However, the computation of a Stein discrepancy can be prohibitive if the Stein operator -- often a sum over likelihood terms or potentials -- is expensive to evaluate. To address this deficiency, we show that stochastic Stein discrepancies (SSDs) based on subsampled approximations of the Stein operator inherit the convergence control properties of standard SDs with probability 1. Along the way, we establish the convergence of Stein variational gradient descent (SVGD) on unbounded domains, resolving an open question of Liu (2017). In our experiments with biased Markov chain Monte Carlo (MCMC) hyperparameter tuning, approximate MCMC sampler selection, and stochastic SVGD, SSDs deliver comparable inferences to standard SDs with orders of magnitude fewer likelihood evaluations.

This paper develops the first theoretical analysis on SVGD.

We introduce a density-power weighted variant for the Stein operator, called the $γ$-Stein operator. This is a novel class of operators derived from the $γ$-divergence, designed to build robust inference methods for unnormalized probability models. The operator's construction (weighting by the model density raised to a positive power $γ$ inherently down-weights the influence of outliers, providing a principled mechanism for robustness. Applying this operator yields a robust generalization of score matching that retains the crucial property of being independent of the model's normalizing constant. We extend this framework to develop two key applications: the $γ$-kernelized Stein discrepancy for robust goodness-of-fit testing, and $γ$-Stein variational gradient descent for robust Bayesian posterior approximation. Empirical results on contaminated Gaussian and quartic potential models show our methods significantly outperform standard baselines in both robustness and statistical efficiency.

Here we show that the operator in Eq. 7 and the corresponding multivariate score-Stein operator in Eq. 2 are equivalent, when they exist; the difference being the factor