We propose in this work RBM-SVGD, a stochastic version of the Stein variational gradient descent (SVGD) method for efficiently sampling from a given probability measure, which is thus useful for Bayesian inference. The method is to apply the random batch method (RBM) for interacting particle systems proposed by Jin et al. to the interacting particle systems in SVGD. While keeping the behaviors of SVGD, it reduces the computational cost, especially when the interacting kernel has long range. We prove that the one marginal distribution of the particles generated by this method converges to the one marginal of the interacting particle systems under Wasserstein-2 distance on fixed time interval $\left[0,T\right]$. Numerical examples verify the efficiency of this new version of SVGD.

我们在这项工作中提出了RBM-SVGD，这是Stein变异梯度下降（SVGD）方法的一种随机版本，可以从给定的概率度量中进行有效采样，因此对于贝叶斯推断很有用。该方法是将随机批处理方法（RBM）用于Jin等人提出的相互作用粒子系统。SVGD中相互作用的粒子系统。在保持SVGD的行为的同时，它降低了计算成本，尤其是在交互内核具有长距离时。我们证明了在固定时间间隔内Wasserstein-2距离下，该方法生成的粒子的一个边际分布收敛到相互作用粒子系统的一个边际。$\left[0，Ť\right]$。数值示例验证了此新版SVGD的效率。