SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence

Stein Variational Gradient Descent (SVGD), a popular sampling algorithm, is\noften described as the kernelized gradient flow for the Kullback-Leibler\ndivergence in the geometry of optimal transport. We introduce a new perspective\non SVGD that instead views SVGD as the (kernelized) gradient flow of the\nchi-squared divergence which, we show, exhibits a strong form of uniform\nexponential ergodicity under conditions as weak as a Poincar\\'e inequality.\nThis perspective leads us to propose an alternative to SVGD, called Laplacian\nAdjusted Wasserstein Gradient Descent (LAWGD), that can be implemented from the\nspectral decomposition of the Laplacian operator associated with the target\ndensity. We show that LAWGD exhibits strong convergence guarantees and good\npractical performance.\n