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SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence
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.
Author Information
Sinho Chewi (Massachusetts Institute of Technology)
Thibaut Le Gouic (Massachusetts Institute of Technology)
Chen Lu (Massachusetts Institute of Technology)
Tyler Maunu (Massachusetts Institute of Technology)
Philippe Rigollet (MIT)
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