Stein Variational Gradient Descent (SVGD), a popular sampling algorithm, is often described as the kernelized gradient flow for the Kullback-Leibler divergence in the geometry of optimal transport. We introduce a new perspective on SVGD that instead views SVGD as the (kernelized) gradient flow of the chi-squared divergence which, we show, exhibits a strong form of uniform exponential ergodicity under conditions as weak as a Poincar\'e inequality. This perspective leads us to propose an alternative to SVGD, called Laplacian Adjusted Wasserstein Gradient Descent (LAWGD), that can be implemented from the spectral decomposition of the Laplacian operator associated with the target density. We show that LAWGD exhibits strong convergence guarantees and good practical performance.

本论文介绍了 Stein Variational Gradient Descent (SVGD) 算法的一种新视角，将 SVGD 视为卡方散度的（核化）梯度流，提出了一种基于目标密度关联的拉普拉斯算子的谱分解实现的替代方法，称为 Laplacian Adjusted Wasserstein Gradient Descent (LAWGD)，这种方法表现出强大的收敛保证和良好的实际性能。

SVGD作为卡方散度的带核Wasserstein梯度流