This research paper addresses the Selective Classification in the presence of Out-of-Distribution (SCOD) problem. It introduces the optimal SCOD strategy involving a Bayes classifier for In-Distribution (ID) data and a linear selector in a 2D space. The study demonstrates that existing OOD detection methods and Softmax Information Retaining Combination (SIRC) provide suboptimal strategies compared to the proposed optimal solution. Additionally, it establishes the non-learnability of SCOD when relying solely on an ID data sample. The introduction of POSCOD, a method for learning the plugin estimate of the optimal SCOD strategy from both ID data and an unlabeled mixture of ID and OOD data, is shown to outperform existing methods.
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