Stein Variational Gradient Descent Without Gradient

摘要

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 introduced 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 all the theoretical properties of SVGD. We shed insights on the empirical choice of the surrogate gradient and further, propose an annealed GF-SVGD that consistently outperforms a number of recent advanced gradient-free MCMC methods in our empirical studies.