  Stein variational gradient descent (SVGD) is a general-purpose
optimization-based sampling algorithm that has recently exploded in popularity,
but is limited by two issues: it is known to produce biased samples, and it can
be slow to converge on complicated distributions. A recently proposed
stochastic variant of SVGD (sSVGD) addresses the first issue, producing
unbiased samples by incorporating a special noise into the SVGD dynamics such
that asymptotic convergence is guaranteed. Meanwhile, Stein variational Newton
(SVN), a Newton-like extension of SVGD, dramatically accelerates the
convergence of SVGD by incorporating Hessian information into the dynamics, but
also produces biased samples. In this paper we derive, and provide a practical
implementation of, a stochastic variant of SVN (sSVN) which is both
asymptotically correct and converges rapidly. We demonstrate the effectiveness
of our algorithm on a difficult class of test problems -- the Hybrid Rosenbrock
density -- and show that sSVN converges using three orders of magnitude fewer
gradient evaluations of the log likelihood than its stochastic SVGD
counterpart. Our results show that sSVN is a promising approach to accelerating
high-precision Bayesian inference tasks with modest-dimension,
$d\sim\mathcal{O}(10)$.
