Stein Variational Gradient Descent Without Gradient

TL;DR

This paper introduces a gradient-free variant of Stein Variational Gradient Descent (SVGD), enabling approximate inference without requiring gradient calculations, and demonstrates its effectiveness through theoretical insights and empirical results.

Contribution

The authors develop GF-SVGD, a novel gradient-free SVGD variant that maintains theoretical properties and improves performance on complex distributions.

Findings

GF-SVGD outperforms recent gradient-free MCMC methods.

The method inherits properties of standard SVGD.

Annealed GF-SVGD enhances performance in high dimensions.

Abstract

Stein variational gradient decent (SVGD) has been shown to be a powerful approximate inference algorithm for complex distributions. However, the standard SVGD requires calculating the gradient of the target density and cannot be applied when the gradient is unavailable. In this work, we develop a gradient-free variant of SVGD (GF-SVGD), which replaces the true gradient with a surrogate gradient, and corrects the induced bias by re-weighting the gradients in a proper form. We show that our GF-SVGD can be viewed as the standard SVGD with a special choice of kernel, and hence directly inherits the theoretical properties of SVGD. We shed insights on the empirical choice of the surrogate gradient and propose an annealed GF-SVGD that leverages the idea of simulated annealing to improve the performance on high dimensional complex distributions. Empirical studies show that our method consistently outperforms a number of recent advanced gradient-free MCMC methods.