Computable Stein discrepancies have been deployed for a variety of applications, including sampler selection in posterior inference, approximate Bayesian inference, and goodness-of-fit testing. Existing convergence-determining Stein discrepancies admit strong theoretical guarantees but suffer from a computational cost that grows quadratically in the sample size. While linear-time Stein discrepancies have been proposed for goodness-of-fit testing, they exhibit avoidable degradations in testing power---even when power is explicitly optimized. To address these shortcomings, we introduce feature Stein discrepancies ($\Phi$SDs), a new family of quality measures that can be cheaply approximated using importance sampling. We show how to construct $\Phi$SDs that provably determine the convergence of a sample to its target and develop high-accuracy approximations---random $\Phi$SDs (R$\Phi$SDs)---which are computable in near-linear time. In our experiments with sampler selection for approximate posterior inference and goodness-of-fit testing, R$\Phi$SDs typically perform as well or better than quadratic-time KSDs while being orders of magnitude faster to compute.

提出了一种新的质量度量方法 - 特征 Stein 差异度量（PhiSD），可通过重要抽样方法进行便宜的近线性逼近，适用于近似后验推断和适配度检验。在实验证明，在速度方面比平方时间差异度量(KSD)更快，可在计算中进行价值代替。

随机特征斯坦差异