In recent years, various interacting particle samplers have been developed to sample from complex target distributions, such as those found in Bayesian inverse problems. These samplers are motivated by the mean-field limit perspective and implemented as ensembles of particles that move in the product state space according to coupled stochastic differential equations. The ensemble approximation and numerical time stepping used to simulate these systems can introduce bias and affect the invariance of the particle system with respect to the target distribution. To correct for this, we investigate the use of a Metropolization step, similar to the Metropolis-adjusted Langevin algorithm. We examine Metropolization of either the whole ensemble or smaller subsets of the ensemble, and prove basic convergence of the resulting ensemble Markov chain to the target distribution. Our numerical results demonstrate the benefits of this correction in numerical examples for popular interacting particle samplers such as ALDI, CBS, and stochastic SVGD.

翻译：近年来，为从复杂目标分布（如贝叶斯反问题中出现的分布）中采样，研究者开发了多种交互粒子采样器。这些采样器受平均场极限理论启发，通过耦合随机微分方程在乘积状态空间中驱动粒子系综运动。然而，用于模拟这些系统的系综逼近和数值时间离散化会引入偏差，影响粒子系统对目标分布的遍历不变性。为消除该误差，本文借鉴Metropolis调整Langevin算法的思想，研究了在采样过程中引入Metropolization步骤的方法。我们分别对整个系综及系综子集实施Metropolization，并证明所得系综马尔可夫链能基本收敛至目标分布。数值实验表明，该校正方法对ALDI、CBS及随机SVGD等主流交互粒子采样器具有显著改进效果。