  Out-of-distribution (OOD) detection is important for deploying machine
learning models in the real world, where test data from shifted distributions
can naturally arise. While a plethora of algorithmic approaches have recently
emerged for OOD detection, a critical gap remains in theoretical understanding.
In this work, we develop an analytical framework that characterizes and unifies
the theoretical understanding for OOD detection. Our analytical framework
motivates a novel OOD detection method for neural networks, GEM, which
demonstrates both theoretical and empirical superiority. In particular, on
CIFAR-100 as in-distribution data, our method outperforms a competitive
baseline by 16.57% (FPR95). Lastly, we formally provide provable guarantees and
comprehensive analysis of our method, underpinning how various properties of
data distribution affect the performance of OOD detection.
