  When deploying a trained machine learning model in the real world, it is
inevitable to receive inputs from out-of-distribution (OOD) sources. For
instance, in continual learning settings, it is common to encounter OOD samples
due to the non-stationarity of a domain. More generally, when we have access to
a set of test inputs, the existing rich line of OOD detection solutions,
especially the recent promise of distance-based methods, falls short in
effectively utilizing the distribution information from training samples and
test inputs. In this paper, we argue that empirical probability distributions
that incorporate geometric information from both training samples and test
inputs can be highly beneficial for OOD detection in the presence of test
inputs available. To address this, we propose to model OOD detection as a
discrete optimal transport problem. Within the framework of optimal transport,
we propose a novel score function known as the \emph{conditional distribution
entropy} to quantify the uncertainty of a test input being an OOD sample. Our
proposal inherits the merits of certain distance-based methods while
eliminating the reliance on distribution assumptions, a-prior knowledge, and
specific training mechanisms. Extensive experiments conducted on benchmark
datasets demonstrate that our method outperforms its competitors in OOD
detection.
