论文标题
SVGD作为卡方发散的核恒星梯度流动
SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence
论文作者
论文摘要
Stein变分梯度下降（SVGD）是一种流行的采样算法，通常被描述为最佳传输几何形状中Kullback-Leibler Divergence的内核梯度流。我们介绍了对SVGD的新观点，相反，它将SVGD视为卡方差异的（内核化）梯度流，我们表明，在像poincaré不平等等弱的条件下，我们表明的是均匀的指数型成态性的强烈形式。这种观点使我们提出了SVGD的替代方案，称为Laplacian调整后的Wasserstein梯度下降（Lawgd），可以从与目标密度相关的Laplacian操作员的光谱分解中实现。我们表明，Lawgd表现出强大的融合保证和良好的实践表现。
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 Poincaré 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.
