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

• URL: http://arxiv.org/abs/2006.02509v1
• Date: Wed, 3 Jun 2020 20:20:21 GMT
• Title: SVGD as a kernelized Wasserstein gradient flow of the chi-squared divergence
• Authors: Sinho Chewi, Thibaut Le Gouic, Chen Lu, Tyler Maunu, Philippe Rigollet
• Abstract summary: Stein Variational Gradient Descent (SVGD) is often described as the kernelized gradient flow for the Kullback-Leibler divergence in the geometry of optimal transport. We show that SVGD exhibits a strong form of uniform exponential ergodicity under conditions as weak as a Poincar'e inequality. We propose Laplacian Adjusted Wasserstein Gradient Descent (LAWGD) that can be implemented from the spectral decomposition of the Laplacian operator associated with the target density.
• Score: 16.864125490806387
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 which, we show, exhibits a strong form of uniform exponential ergodicity under conditions as weak as a Poincar\'e 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.

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