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Stein Variational Gradient Descent (SVGD) is a popular sampling algorithmused in various machine learning tasks. It is well known that SVGD arises froma discretization of the kernelized gradient flow of the Kullback-Leiblerdivergence $D_{KL}\left(\cdot\mid\pi\right)$, where $\pi$ is the targetdistribution. In this work, we propose to enhance SVGD via the introduction ofimportance weights, which leads to a new method for which we coin the name$\beta$-SVGD. In the continuous time and infinite particles regime, the timefor this flow to converge to the equilibrium distribution $\pi$, quantified bythe Stein Fisher information, depends on $\rho_0$ and $\pi$ very weakly. Thisis very different from the kernelized gradient flow of Kullback-Leiblerdivergence, whose time complexity depends on$D_{KL}\left(\rho_0\mid\pi\right)$. Under certain assumptions, we provide adescent lemma for the population limit $\beta$-SVGD, which covers the descentlemma for the population limit SVGD when $\beta\to 0$. We also illustrate theadvantages of $\beta$-SVGD over SVGD by experiments.

Improved Stein Variational Gradient Descent with Importance Weights