Kernel Selection for Stein Variational Gradient Descent

Stein variational gradient descent (SVGD) and its variants have shown promising successes in approximate inference for complex distributions. However, their empirical performance depends crucially on the choice of optimal kernel. Unfortunately, RBF kernel with median heuristics is a common choice in previous approaches which has been proved sub-optimal. Inspired by the paradigm of multiple kernel learning, our solution to this issue is using a combination of multiple kernels to approximate the optimal kernel instead of a single one which may limit the performance and flexibility. To do so, we extend Kernelized Stein Discrepancy (KSD) to its multiple kernel view called Multiple Kernelized Stein Discrepancy (MKSD). Further, we leverage MKSD to construct a general algorithm based on SVGD, which be called Multiple Kernel SVGD (MK-SVGD). Besides, we automatically assign a weight to each kernel without any other parameters. The proposed method not only gets rid of optimal kernel dependence but also maintains computational effectiveness. Experiments on various tasks and models show the effectiveness of our method.