Improved Stein Variational Gradient Descent with Importance Weights

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 ( · | π ) , where π 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 β -SVGD . In the continuous time and infinite particles regime, the time for this flow to converge to the equilibrium distribution π , quantified by the Stein Fisher information, depends on ρ 0 and π very weakly. This is very different from the kernelized gradient flow of Kullback-Leibler divergence, whose time complexity depends on D KL ( ρ 0 | π ) . Under certain assumptions, we provide a descent lemma for the population limit β -SVGD , which covers the descent lemma for the population limit SVGD when β → 0 . We also illustrate the advantages of β -SVGD over SVGD by simple experiments.