  Bayesian inference on structured models typically relies on the ability to
infer posterior distributions of underlying hidden variables. However,
inference in implicit models or complex posterior distributions is hard. A
popular tool for learning implicit models are generative adversarial networks
(GANs) which learn parameters of generators by fooling discriminators.
Typically, GANs are considered to be models themselves and are not understood
in the context of inference. Current techniques rely on inefficient global
discrimination of joint distributions to perform learning, or only consider
discriminating a single output variable. We overcome these limitations by
treating GANs as a basis for likelihood-free inference in generative models and
generalize them to Bayesian posterior inference over factor graphs. We propose
local learning rules based on message passing minimizing a global divergence
criterion involving cooperating local adversaries used to sidestep explicit
likelihood evaluations. This allows us to compose models and yields a unified
inference and learning framework for adversarial learning. Our framework treats
model specification and inference separately and facilitates richly structured
models within the family of Directed Acyclic Graphs, including components such
as intractable likelihoods, non-differentiable models, simulators and generally
cumbersome models. A key result of our treatment is the insight that Bayesian
inference on structured models can be performed only with sampling and
discrimination when using nonparametric variational families, without access to
explicit distributions. As a side-result, we discuss the link to likelihood
maximization. These approaches hold promise to be useful in the toolbox of
probabilistic modelers and enrich the gamut of current probabilistic
programming applications.
