Reject option models comprising out-of-distribution detection

The optimal prediction strategy for out-of-distribution (OOD) setups is a fundamental question in machine learning. In this paper, we address this question and present several contributions. We propose three reject option models for OOD setups: the Cost-based model, the Bounded TPR-FPR model, and the Bounded Precision-Recall model. These models extend the standard reject option models used in non-OOD setups and define the notion of an optimal OOD selective classifier. We establish that all the proposed models, despite their different formulations, share a common class of optimal strategies. Motivated by the optimal strategy, we introduce double-score OOD methods that leverage uncertainty scores from two chosen OOD detectors: one focused on OOD/ID discrimination and the other on misclassification detection. The experimental results consistently demonstrate the superior performance of this simple strategy compared to state-of-the-art methods. Additionally, we propose novel evaluation metrics derived from the definition of the optimal strategy under the proposed OOD rejection models. These new metrics provide a comprehensive and reliable assessment of OOD methods without the deficiencies observed in existing evaluation approaches.