Conformal prediction is a general distribution-free approach for constructing prediction sets combined with any machine learning algorithm that achieve valid marginal or conditional coverage in finite samples. Ordinal classification is common in real applications where the target variable has natural ordering among the class labels. In this paper, we discuss constructing distribution-free prediction sets for such ordinal classification problems by leveraging the ideas of conformal prediction and multiple testing with FWER control. Newer conformal prediction methods are developed for constructing contiguous and non-contiguous prediction sets based on marginal and conditional (class-specific) conformal $p$-values, respectively. Theoretically, we prove that the proposed methods respectively achieve satisfactory levels of marginal and class-specific conditional coverages. Through simulation study and real data analysis, these proposed methods show promising performance compared to the existing conformal method.

翻译：共形预测是一种通用的无分布方法，可与任何机器学习算法结合构建预测集，在有限样本中实现有效的边际覆盖或条件覆盖。序贯分类在现实应用中十分常见，其目标变量在类别标签间具有自然顺序关系。本文探讨如何利用共形预测与基于族系错误率控制的多重检验思想，为这类序贯分类问题构建无分布预测集。我们分别基于边际共形$p$值和条件（类别特定）共形$p$值，发展了构建连续与非连续预测集的新型共形预测方法。理论上，我们证明了所提方法能分别达到令人满意的边际覆盖水平与类别特定条件覆盖水平。通过模拟研究与真实数据分析，与现有共形方法相比，这些新方法展现出更优的性能。