  Deep autoregressive models compute point likelihood estimates of individual
data points. However, many applications (i.e., database cardinality estimation)
require estimating range densities, a capability that is under-explored by
current neural density estimation literature. In these applications, fast and
accurate range density estimates over high-dimensional data directly impact
user-perceived performance. In this paper, we explore a technique, variable
skipping, for accelerating range density estimation over deep autoregressive
models. This technique exploits the sparse structure of range density queries
to avoid sampling unnecessary variables during approximate inference. We show
that variable skipping provides 10-100$\times$ efficiency improvements when
targeting challenging high-quantile error metrics, enables complex applications
such as text pattern matching, and can be realized via a simple data
augmentation procedure without changing the usual maximum likelihood objective.
