  We propose a novel adaptive importance sampling algorithm which incorporates
Stein variational gradient decent algorithm (SVGD) with importance sampling
(IS). Our algorithm leverages the nonparametric transforms in SVGD to
iteratively decrease the KL divergence between our importance proposal and the
target distribution. The advantages of this algorithm are twofold: first, our
algorithm turns SVGD into a standard IS algorithm, allowing us to use standard
diagnostic and analytic tools of IS to evaluate and interpret the results;
second, we do not restrict the choice of our importance proposal to predefined
distribution families like traditional (adaptive) IS methods. Empirical
experiments demonstrate that our algorithm performs well on evaluating
partition functions of restricted Boltzmann machines and testing likelihood of
variational auto-encoders.
