  Recent work has shown that deep generative models can assign higher
likelihood to out-of-distribution data sets than to their training data
(Nalisnick et al., 2019; Choi et al., 2019). We posit that this phenomenon is
caused by a mismatch between the model's typical set and its areas of high
probability density. In-distribution inputs should reside in the former but not
necessarily in the latter, as previous work has presumed. To determine whether
or not inputs reside in the typical set, we propose a statistically principled,
easy-to-implement test using the empirical distribution of model likelihoods.
The test is model agnostic and widely applicable, only requiring that the
likelihood can be computed or closely approximated. We report experiments
showing that our procedure can successfully detect the out-of-distribution sets
in several of the challenging cases reported by Nalisnick et al. (2019).

Machine Learning;Machine Learning