  Unsupervised out-of-distribution (U-OOD) detection has recently attracted
much attention due its importance in mission-critical systems and broader
applicability over its supervised counterpart. Despite this increase in
attention, U-OOD methods suffer from important shortcomings. By performing a
large-scale evaluation on different benchmarks and image modalities, we show in
this work that most popular state-of-the-art methods are unable to consistently
outperform a simple anomaly detector based on pre-trained features and the
Mahalanobis distance (MahaAD). A key reason for the inconsistencies of these
methods is the lack of a formal description of U-OOD. Motivated by a simple
thought experiment, we propose a characterization of U-OOD based on the
invariants of the training dataset. We show how this characterization is
unknowingly embodied in the top-scoring MahaAD method, thereby explaining its
quality. Furthermore, our approach can be used to interpret predictions of
U-OOD detectors and provides insights into good practices for evaluating future
U-OOD methods.
