  Modern neural networks can assign high confidence to inputs drawn from
outside the training distribution, posing threats to models in real-world
deployments. While much research attention has been placed on designing new
out-of-distribution (OOD) detection methods, the precise definition of OOD is
often left in vagueness and falls short of the desired notion of OOD in
reality. In this paper, we present a new formalization and model the data
shifts by taking into account both the invariant and environmental (spurious)
features. Under such formalization, we systematically investigate how spurious
correlation in the training set impacts OOD detection. Our results suggest that
the detection performance is severely worsened when the correlation between
spurious features and labels is increased in the training set. We further show
insights on detection methods that are more effective in reducing the impact of
spurious correlation and provide theoretical analysis on why reliance on
environmental features leads to high OOD detection error. Our work aims to
facilitate a better understanding of OOD samples and their formalization, as
well as the exploration of methods that enhance OOD detection.
