Recently, there has been immense research interest in the use of *implicit
probabilistic models* in machine learning. Implicit models are an attractive
alternative to *prescribed* models, not least due to its capacity to admit high
fidelity to the data generating process.

However, this level of expressiveness places significant analytical burdens on
their inference, since they fail to yield tractable probability densities.
Although current predominant methods such as *variational inference* have become
indispensable tools for efficient and scalable inference in highly-complex
models, their classical approaches are ill-equipped to deal with the
intractabilities posed by implicit models.

We are just beginning to understand the implications of learning in implicit
models, and appreciate their formal connections to *density ratio estimation*
and *approximate divergence minimization*.
This understanding has helped us to dramatically expand the scope and
applicability of variational inference, which can now be applied in settings
where no likelihood is available, where the family of posterior approximations
is arbitrarily complex, and indeed, even where no prior density is available.

These efforts to generalize have made it feasible to perform approximate Bayesian inference in a vastly richer class of probabilistic models. The aim of this research is further advance these techniques, and to also provide a better theoretical understanding of the newly-proposed approaches.