  Particle-based approximate Bayesian inference approaches such as Stein
Variational Gradient Descent (SVGD) combine the flexibility and convergence
guarantees of sampling methods with the computational benefits of variational
inference. In practice, SVGD relies on the choice of an appropriate kernel
function, which impacts its ability to model the target distribution -- a
challenging problem with only heuristic solutions. We propose Neural
Variational Gradient Descent (NVGD), which is based on parameterizing the
witness function of the Stein discrepancy by a deep neural network whose
parameters are learned in parallel to the inference, mitigating the necessity
to make any kernel choices whatsoever. We empirically evaluate our method on
popular synthetic inference problems, real-world Bayesian linear regression,
and Bayesian neural network inference.
