Semantic or Covariate? A Study on the Intractable Case of Out-of-Distribution Detection
This work addresses a foundational problem in machine learning for researchers and practitioners in OOD detection, clarifying theoretical limits to improve evaluation and method development.
The paper tackles the ambiguity in defining semantic shifts for out-of-distribution (OOD) detection, leading to intractable testing protocols, by proposing precise definitions of Semantic and Covariate Spaces and a 'Tractable OOD' setting to ensure distinguishability, with experiments validating their theorems.
The primary goal of out-of-distribution (OOD) detection tasks is to identify inputs with semantic shifts, i.e., if samples from novel classes are absent in the in-distribution (ID) dataset used for training, we should reject these OOD samples rather than misclassifying them into existing ID classes. However, we find the current definition of "semantic shift" is ambiguous, which renders certain OOD testing protocols intractable for the post-hoc OOD detection methods based on a classifier trained on the ID dataset. In this paper, we offer a more precise definition of the Semantic Space and the Covariate Space for the ID distribution, allowing us to theoretically analyze which types of OOD distributions make the detection task intractable. To avoid the flaw in the existing OOD settings, we further define the "Tractable OOD" setting which ensures the distinguishability of OOD and ID distributions for the post-hoc OOD detection methods. Finally, we conduct several experiments to demonstrate the necessity of our definitions and validate the correctness of our theorems.