  Models that employ latent variables to capture structure in observed data lie
at the heart of many current unsupervised learning algorithms, but exact
maximum-likelihood learning for powerful and flexible latent-variable models is
almost always intractable. Thus, state-of-the-art approaches either abandon the
maximum-likelihood framework entirely, or else rely on a variety of variational
approximations to the posterior distribution over the latents. Here, we propose
an alternative approach that we call amortised learning. Rather than computing
an approximation to the posterior over latents, we use a wake-sleep Monte-Carlo
strategy to learn a function that directly estimates the maximum-likelihood
parameter updates. Amortised learning is possible whenever samples of latents
and observations can be simulated from the generative model, treating the model
as a "black box". We demonstrate its effectiveness on a wide range of complex
models, including those with latents that are discrete or supported on
non-Euclidean spaces.
