Improved Stein Variational Gradient Descent with Importance Weights

Abstract

Stein Variational Gradient Descent (SVGD) is a popular sampling algorithm used in various machine learning tasks. It is well known that SVGD arises from a discretization of the kernelized gradient flow of the Kullback-Leibler divergence D_KL(), where is the target distribution. In this work, we propose to enhance SVGD via the introduction of importance weights, which leads to a new method for which we coin the name -SVGD. In the continuous time and infinite particles regime, the time for this flow to converge to the equilibrium distribution , quantified by the Stein Fisher information, depends on _0 and very weakly. This is very different from the kernelized gradient flow of Kullback-Leibler divergence, whose time complexity depends on D_KL(_0). Under certain assumptions, we provide a descent lemma for the population limit -SVGD, which covers the descent lemma for the population limit SVGD when 0. We also illustrate the advantages of -SVGD over SVGD by experiments.

Tasks

Reproductions