Detecting Out-of-Distribution Samples via Conditional Distribution Entropy with Optimal Transport

Abstract

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.