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

Part of Advances in Neural Information Processing Systems 33 (NeurIPS 2020)

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Sinho Chewi, Thibaut Le Gouic, Chen Lu, Tyler Maunu, Philippe Rigollet


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. Motivated by this perspective, we provide a convergence analysis of the chi-squared gradient flow. We also show that our new perspective provides better guidelines for choosing effective kernels for SVGD.