  A key design constraint when implementing Monte Carlo and variational
inference algorithms is that it must be possible to cheaply and exactly
evaluate the marginal densities of proposal distributions and variational
families. This takes many interesting proposals off the table, such as those
based on involved simulations or stochastic optimization. This paper broadens
the design space, by presenting a framework for applying Monte Carlo and
variational inference algorithms when proposal densities cannot be exactly
evaluated. Our framework, recursive auxiliary-variable inference (RAVI),
instead approximates the necessary densities using meta-inference: an
additional layer of Monte Carlo or variational inference, that targets the
proposal, rather than the model. RAVI generalizes and unifies several existing
methods for inference with expressive approximating families, which we show
correspond to specific choices of meta-inference algorithm, and provides new
theory for analyzing their bias and variance. We illustrate RAVI's design
framework and theorems by using them to analyze and improve upon Salimans et
al.'s Markov Chain Variational Inference, and to design a novel sampler for
Dirichlet process mixtures, achieving state-of-the-art results on a standard
benchmark dataset from astronomy and on a challenging datacleaning task with
Medicare hospital data.
