  Bayesian inference problems require sampling or approximating
high-dimensional probability distributions. The focus of this paper is on the
recently introduced Stein variational gradient descent methodology, a class of
algorithms that rely on iterated steepest descent steps with respect to a
reproducing kernel Hilbert space norm. This construction leads to interacting
particle systems, the mean-field limit of which is a gradient flow on the space
of probability distributions equipped with a certain geometrical structure. We
leverage this viewpoint to shed some light on the convergence properties of the
algorithm, in particular addressing the problem of choosing a suitable positive
definite kernel function. Our analysis leads us to considering certain
nondifferentiable kernels with adjusted tails. We demonstrate significant
performance gains of these in various numerical experiments.
