On the geometry of Stein variational gradient descent

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 …

algorithm algorithms bayesian bayesian inference construction convergence flow focus geometry gradient inference kernel leads light mean methodology paper probability sampling space systems