This paper addresses the problem of designing reliable prediction models that
abstain from predictions when faced with uncertain or out-of-distribution
samples - a recently proposed problem known as Selective Classification in the
presence of Out-of-Distribution data (SCOD). We make three key contributions to
SCOD. Firstly, we demonstrate that the optimal SCOD strategy involves a Bayes
classifier for in-distribution (ID) data and a selector represented as a
stochastic linear classifier in a 2D space, using i) the conditional risk of
the ID classifier, and ii) the likelihood ratio of ID and out-of-distribution
(OOD) data as input. This contrasts with suboptimal strategies from current OOD
detection methods and the Softmax Information Retaining Combination (SIRC),
specifically developed for SCOD. Secondly, we establish that in a
distribution-free setting, the SCOD problem is not Probably Approximately
Correct learnable when relying solely on an ID data sample. Third, we introduce
POSCOD, a simple method for learning a plugin estimate of the optimal SCOD
strategy from both an ID data sample and an unlabeled mixture of ID and OOD
data. Our empirical results confirm the theoretical findings and demonstrate
that our proposed method, POSCOD, out performs existing OOD methods in
effectively addressing the SCOD problem.

在存在外部样本时面临选择性分类问题的可靠预测模型的设计，我们提出了三个关键贡献。首先，我们证明最优的 SCOD 策略采用了贝叶斯分类器用于分布内数据和一个在二维空间表示为随机线性分类器的选择器，利用了分布内分类器的条件风险和分布内外数据的似然比作为输入，与当前的分布外检测方法和专门针对 SCOD 开发的 Softmax 信息保留组合（SIRC）方法的次优策略不同。其次，我们证明在一个无分布设置下，只依赖分布内数据样本时 SCOD 问题无法以近似正确学习。第三，我们引入了 POSCOD，一种简单的方法，从分布内数据样本和无标签的分布内外数据混合中学习最优 SCOD 策略的插件估计。我们的实证结果验证了理论发现，并证明我们提出的方法 POSCOD 在有效解决 SCOD 问题上优于现有的分布外方法。