  This document aims to provide a review on learning with deep generative
models (DGMs), which is an highly-active area in machine learning and more
generally, artificial intelligence. This review is not meant to be a tutorial,
but when necessary, we provide self-contained derivations for completeness.
This review has two features. First, though there are different perspectives to
classify DGMs, we choose to organize this review from the perspective of
graphical modeling, because the learning methods for directed DGMs and
undirected DGMs are fundamentally different. Second, we differentiate model
definitions from model learning algorithms, since different learning algorithms
can be applied to solve the learning problem on the same model, and an
algorithm can be applied to learn different models. We thus separate model
definition and model learning, with more emphasis on reviewing, differentiating
and connecting different learning algorithms. We also discuss promising future
research directions.
