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

Variable Skipping for Autoregressive Range Density Estimation