As a natural extension to the standard conformal prediction method, several conformal risk control methods have been recently developed and applied to various learning problems. In this work, we seek to control the conformal risk in expectation for ordinal classification tasks, which have broad applications to many real problems. For this purpose, we firstly formulated the ordinal classification task in the conformal risk control framework, and provided theoretic risk bounds of the risk control method. Then we proposed two types of loss functions specially designed for ordinal classification tasks, and developed corresponding algorithms to determine the prediction set for each case to control their risks at a desired level. We demonstrated the effectiveness of our proposed methods, and analyzed the difference between the two types of risks on three different datasets, including a simulated dataset, the UTKFace dataset and the diabetic retinopathy detection dataset.

翻译：作为标准保形预测方法的自然扩展，近年来开发了多种保形风险控制方法，并将其应用于各类学习问题。本文针对广泛适用于众多实际问题的有序分类任务，旨在控制其保形风险的期望值。为此，我们首先将有序分类任务纳入保形风险控制框架，并给出了风险控制方法的理论风险界限。随后，我们提出了两种专门针对有序分类任务设计的损失函数，并开发了相应算法以确定每种情况下的预测集，从而将风险控制在期望水平。我们在三个不同数据集（包括模拟数据集、UTKFace数据集和糖尿病视网膜病变检测数据集）上验证了所提方法的有效性，并分析了两种风险类型之间的差异。