  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.
