Semantic or Covariate? A Study on the Intractable Case of Out-of-Distribution Detection

TL;DR

A more precise definition of the Semantic Space and the Covariate Space for the ID distribution is offered, allowing us to theoretically analyze which types of OOD distributions make the detection task intractable.

Abstract

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.

Figures (8)

• Figure 1: An illustration of the intractable OOD detection setting. (a) shows two training setups and two testing protocols. After being trained under the "breed-aggregated" setup, the model will struggle to identify a novel dog breed in the "OOD-breed" testing protocol. (b) demonstrates the feature distribution in this intractable case, where the ID classes are well-separated along the object-specific feature, while the OOD class differs from the ID classes only along the breed-specific feature dimension.
• Figure 2: Visualization of the weight matrix $\boldsymbol{W}$ in the linear classifier: (a) the final optimized weight matrix, (b) the variations of the weights for each input dimension corresponding to the first class.
• Figure 3: The distributions of EBO's EBO_2020 confidence output under two training setups. In the "breed-separated" training setup, the confidence distributions for ID and OOD dogs show a significant difference, while in the "breed-aggregated" training setup, the two confidence distributions are almost overlapping.
• Figure 4: The ID classification ACC and the OOD detection AUROC of EBO during the training process. The OOD detection performance rises along with the ID classification performance in the "breed-separated" training setup. However, the OOD detection AUROC remains around 50% under the "breed-aggregated" training setup.
• Figure 5: The t-SNE visualization of the features of ID and OOD dogs extracted by the ResNet-18 trained under "breed-separated" and "breed-aggregated" setups. The separability between OOD and ID features in the "breed-separated" setup is significantly higher than in the "breed-aggregated" setup.