NeurIPS 2020poster90 citations
SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence
Sinho Chewi, Thibaut Le Gouic, Chen Lu, Tyler Maunu, Philippe Rigollet
Abstract
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.
BibTeX
@inproceedings{NEURIPS2020_16f8e136,
author = {Chewi, Sinho and Le Gouic, Thibaut and Lu, Chen and Maunu, Tyler and Rigollet, Philippe},
booktitle = {Advances in Neural Information Processing Systems},
editor = {H. Larochelle and M. Ranzato and R. Hadsell and M.F. Balcan and H. Lin},
pages = {2098--2109},
publisher = {Curran Associates, Inc.},
title = {SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence},
url = {https://proceedings.neurips.cc/paper_files/paper/2020/file/16f8e136ee5693823268874e58795216-Paper.pdf},
volume = {33},
year = {2020}
}