用消息传递方法优化采样，提升多变量分布采样质量。
Low Stein Discrepancy via Message-Passing Monte Carlo
- 基于消息传递框架，构建低差异采样新方法。
- 在多个数据集上实现更低的核化Stein差异值。
- 适合需要高质量采样的生成模型与贝叶斯推断场景。
消息传递蒙特卡洛（MPMC）是一种利用几何深度学习工具的新颖低差异采样方法。虽然最初用于生成均匀点集，本文将其扩展至从已知概率密度函数的多变量分布中采样。所提出的斯坦因-消息传递蒙特卡洛（Stein-MPMC）方法通过最小化核化斯坦因差异，确保了更高的采样质量。实验表明，Stein-MPMC在多个基准测试中优于斯坦因变分梯度下降和（贪婪）斯坦因点等现有方法，实现了更低的斯坦因差异值。
原文摘要 · Abstract (English)
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.
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