  Order-agnostic autoregressive distribution (density) estimation (OADE), i.e.,
autoregressive distribution estimation where the features can occur in an
arbitrary order, is a challenging problem in generative machine learning. Prior
work on OADE has encoded feature identity by assigning each feature to a
distinct fixed position in an input vector. As a result, architectures built
for these inputs must strategically mask either the input or model weights to
learn the various conditional distributions necessary for inferring the full
joint distribution of the dataset in an order-agnostic way. In this paper, we
propose an alternative approach for encoding feature identities, where each
feature's identity is included alongside its value in the input. This feature
identity encoding strategy allows neural architectures designed for sequential
data to be applied to the OADE task without modification. As a proof of
concept, we show that a Transformer trained on this input (which we refer to as
"the DEformer", i.e., the distribution estimating Transformer) can effectively
model binarized-MNIST, approaching the performance of fixed-order
autoregressive distribution estimating algorithms while still being entirely
order-agnostic. Additionally, we find that the DEformer surpasses the
performance of recent flow-based architectures when modeling a tabular dataset.
