  Recent research has seen several advances relevant to black-box VI, but the
current state of automatic posterior inference is unclear. One such advance is
the use of normalizing flows to define flexible posterior densities for deep
latent variable models. Another direction is the integration of Monte-Carlo
methods to serve two purposes; first, to obtain tighter variational objectives
for optimization, and second, to define enriched variational families through
sampling. However, both flows and variational Monte-Carlo methods remain
relatively unexplored for black-box VI. Moreover, on a pragmatic front, there
are several optimization considerations like step-size scheme, parameter
initialization, and choice of gradient estimators, for which there are no clear
guidance in the existing literature. In this paper, we postulate that black-box
VI is best addressed through a careful combination of numerous algorithmic
components. We evaluate components relating to optimization, flows, and
Monte-Carlo methods on a benchmark of 30 models from the Stan model library.
The combination of these algorithmic components significantly advances the
state-of-the-art "out of the box" variational inference.
