Stein Variational Gradient Descent (SVGD) is a popular particle-based method for Bayesian inference. However, its convergence suffers from the variance collapse, which reduces the accuracy and diversity of the estimation. In this paper, we study the isotropy property of finite particles during the convergence process and show that SVGD of finite particles cannot spread across the entire sample space. Instead, all particles tend to cluster around the particle center within a certain range and we provide an analytical bound for this cluster. To further improve the effectiveness of SVGD for high-dimensional problems, we propose the Augmented Message Passing SVGD (AUMP-SVGD) method, which is a two-stage optimization procedure that does not require sparsity of the target distribution, unlike the MP-SVGD method. Our algorithm achieves satisfactory accuracy and overcomes the variance collapse problem in various benchmark problems.

翻译：施泰因变分梯度下降（SVGD）是一种流行的基于粒子的贝叶斯推断方法。然而，其收敛过程受到方差崩溃问题的影响，降低了估计的准确性和多样性。本文研究了有限粒子在收敛过程中的各向同性性质，并证明了有限粒子的SVGD无法覆盖整个样本空间，所有粒子倾向于聚集在以粒子中心为中心的特定范围内，我们给出了该聚集范围的分析边界。为了进一步提升SVGD在高维问题中的有效性，我们提出了增强消息传递SVGD（AUMP-SVGD）方法，这是一种两阶段优化过程，与MP-SVGD方法不同，它不需要目标分布具有稀疏性。我们的算法在各种基准测试中实现了令人满意的准确性，并克服了方差崩溃问题。