Message-Passing Monte Carlo (MPMC) was recently introduced as a novel low-discrepancy sampling approach leveraging tools from geometric deep learning. While originally designed for generating uniform point sets, we extend this framework to sample from general multivariate probability distributions with known probability density function. Our proposed method, Stein-Message-Passing Monte Carlo (Stein-MPMC), minimizes a kernelized Stein discrepancy, ensuring improved sample quality. Finally, we show that Stein-MPMC outperforms competing methods, such as Stein Variational Gradient Descent and (greedy) Stein Points, by achieving a lower Stein discrepancy.

翻译：消息传递蒙特卡洛（MPMC）是近期提出的一种新颖的低差异采样方法，它利用了几何深度学习中的工具。虽然最初设计用于生成均匀点集，但我们将此框架扩展至从已知概率密度函数的一般多元概率分布中进行采样。我们提出的方法——斯坦因消息传递蒙特卡洛（Stein-MPMC）——最小化了核化斯坦因差异，从而确保了更高的样本质量。最后，我们证明 Stein-MPMC 通过实现更低的斯坦因差异，其性能优于斯坦因变分梯度下降和（贪婪）斯坦因点等竞争方法。