Selective classification enhances the reliability of predictive models by allowing them to abstain from making uncertain predictions. In this work, we revisit the design of optimal selection functions through the lens of the Neyman--Pearson lemma, a classical result in statistics that characterizes the optimal rejection rule as a likelihood ratio test. We show that this perspective not only unifies the behavior of several post-hoc selection baselines, but also motivates new approaches to selective classification which we propose here. A central focus of our work is the setting of covariate shift, where the input distribution at test time differs from that at training. This realistic and challenging scenario remains relatively underexplored in the context of selective classification. We evaluate our proposed methods across a range of vision and language tasks, including both supervised learning and vision-language models. Our experiments demonstrate that our Neyman--Pearson-informed methods consistently outperform existing baselines, indicating that likelihood ratio-based selection offers a robust mechanism for improving selective classification under covariate shifts. Our code is publicly available at https://github.com/clear-nus/sc-likelihood-ratios.

翻译：选择性分类通过允许模型在不确定时弃权预测，从而提升预测模型的可靠性。本文从统计学经典结论——奈曼-皮尔逊引理——的视角重新审视最优选择函数的设计，该引理将最优拒绝规则刻画为似然比检验。我们证明这一视角不仅能统一多种后验选择基线的行为，还启发了本文提出的选择性分类新方法。研究的核心关注点是协变量偏移场景，即测试时的输入分布与训练时存在差异。这一现实且具有挑战性的情境在选择性分类领域尚未得到充分探索。我们在包括监督学习和视觉-语言模型在内的多类视觉与语言任务中评估了所提方法。实验结果表明，基于奈曼-皮尔逊理论的方法在协变量偏移下持续优于现有基线，表明基于似然比的选择机制为改进选择性分类提供了稳健方案。代码已公开于 https://github.com/clear-nus/sc-likelihood-ratios。