  Neural density estimators are flexible families of parametric models which
have seen widespread use in unsupervised machine learning in recent years.
Maximum-likelihood training typically dictates that these models be constrained
to specify an explicit density. However, this limitation can be overcome by
instead using a neural network to specify an energy function, or unnormalized
density, which can subsequently be normalized to obtain a valid distribution.
The challenge with this approach lies in accurately estimating the normalizing
constant of the high-dimensional energy function. We propose the Autoregressive
Energy Machine, an energy-based model which simultaneously learns an
unnormalized density and computes an importance-sampling estimate of the
normalizing constant for each conditional in an autoregressive decomposition.
The Autoregressive Energy Machine achieves state-of-the-art performance on a
suite of density-estimation tasks.
