  Stein variational gradient descent (SVGD) and its variants have shown
promising successes in approximate inference for complex distributions. In
practice, we notice that the kernel used in SVGD-based methods has a decisive
effect on the empirical performance. Radial basis function (RBF) kernel with
median heuristics is a common choice in previous approaches, but unfortunately
this has proven to be sub-optimal. Inspired by the paradigm of Multiple Kernel
Learning (MKL), our solution to this flaw is using a combination of multiple
kernels to approximate the optimal kernel, rather than a single one which may
limit the performance and flexibility. Specifically, we first extend Kernelized
Stein Discrepancy (KSD) to its multiple kernels view called Multiple Kernelized
Stein Discrepancy (MKSD) and then leverage MKSD to construct a general
algorithm Multiple Kernel SVGD (MK-SVGD). Further, MKSVGD can automatically
assign a weight to each kernel without any other parameters, which means that
our method not only gets rid of optimal kernel dependence but also maintains
computational efficiency. Experiments on various tasks and models demonstrate
that our proposed method consistently matches or outperforms the competing
methods.
