  Bayesian computation plays an important role in modern machine learning and
statistics to reason about uncertainty. A key computational challenge in
Bayesian inference is to develop efficient techniques to approximate, or draw
samples from posterior distributions. Stein variational gradient decent (SVGD)
has been shown to be a powerful approximate inference algorithm for this issue.
However, the vanilla SVGD requires calculating the gradient of the target
density and cannot be applied when the gradient is unavailable or too expensive
to evaluate. In this paper we explore one way to address this challenge by the
construction of a local surrogate for the target distribution in which the
gradient can be obtained in a much more computationally feasible manner. More
specifically, we approximate the forward model using a deep neural network
(DNN) which is trained on a carefully chosen training set, which also
determines the quality of the surrogate. To this end, we propose a general
adaptation procedure to refine the local approximation online without
destroying the convergence of the resulting SVGD. This significantly reduces
the computational cost of SVGD and leads to a suite of algorithms that are
straightforward to implement. The new algorithm is illustrated on a set of
challenging Bayesian inverse problems, and numerical experiments demonstrate a
clear improvement in performance and applicability of standard SVGD.
