  We study the problem of efficiently detecting Out-of-Distribution (OOD)
samples at test time in supervised and unsupervised learning contexts. While ML
models are typically trained under the assumption that training and test data
stem from the same distribution, this is often not the case in realistic
settings, thus reliably detecting distribution shifts is crucial at deployment.
We re-formulate the OOD problem under the lenses of statistical testing and
then discuss conditions that render the OOD problem identifiable in statistical
terms. Building on this framework, we study convergence guarantees of an OOD
test based on the Wasserstein distance, and provide a simple empirical
evaluation.
