  Auto-encoding generative adversarial networks (GANs) combine the standard GAN
algorithm, which discriminates between real and model-generated data, with a
reconstruction loss given by an auto-encoder. Such models aim to prevent mode
collapse in the learned generative model by ensuring that it is grounded in all
the available training data. In this paper, we develop a principle upon which
auto-encoders can be combined with generative adversarial networks by
exploiting the hierarchical structure of the generative model. The underlying
principle shows that variational inference can be used a basic tool for
learning, but with the in- tractable likelihood replaced by a synthetic
likelihood, and the unknown posterior distribution replaced by an implicit
distribution; both synthetic likelihoods and implicit posterior distributions
can be learned using discriminators. This allows us to develop a natural fusion
of variational auto-encoders and generative adversarial networks, combining the
best of both these methods. We describe a unified objective for optimization,
discuss the constraints needed to guide learning, connect to the wide range of
existing work, and use a battery of tests to systematically and quantitatively
assess the performance of our method.
