  We propose a general purpose variational inference algorithm that forms a
natural counterpart of gradient descent for optimization. Our method
iteratively transports a set of particles to match the target distribution, by
applying a form of functional gradient descent that minimizes the KL
divergence. Empirical studies are performed on various real world models and
datasets, on which our method is competitive with existing state-of-the-art
methods. The derivation of our method is based on a new theoretical result that
connects the derivative of KL divergence under smooth transforms with Stein's
identity and a recently proposed kernelized Stein discrepancy, which is of
independent interest.
