  Deep generative models have been demonstrated as state-of-the-art density
estimators. Yet, recent work has found that they often assign a higher
likelihood to data from outside the training distribution. This seemingly
paradoxical behavior has caused concerns over the quality of the attained
density estimates. In the context of hierarchical variational autoencoders, we
provide evidence to explain this behavior by out-of-distribution data having
in-distribution low-level features. We argue that this is both expected and
desirable behavior. With this insight in hand, we develop a fast, scalable and
fully unsupervised likelihood-ratio score for OOD detection that requires data
to be in-distribution across all feature-levels. We benchmark the method on a
vast set of data and model combinations and achieve state-of-the-art results on
out-of-distribution detection.
