We apply conformal prediction techniques to regression problems with circular responses, producing prediction sets with adaptive arc length and finite-sample coverage guarantees for any circular predictive model under the assumption of data exchangeability. Leveraging the high performance of existing predictive models designed for linear responses, we analyze a general projection procedure that converts any linear-response regression model into one suitable for circular responses. When random forests are used as base models in this projection procedure, we leverage the random forest out-of-bag mechanism to eliminate the need for a separate calibration sample in the construction of prediction sets. On synthetic and real datasets, the resulting projected random forest model produces more efficient out-of-bag conformal prediction sets, with shorter median arc length, than the split conformal prediction sets generated by two existing alternative models.

翻译：我们将共形预测技术应用于具有圆响应的回归问题，构建具有自适应弧长且在数据可交换性假设下对任何圆预测模型提供有限样本覆盖保证的预测集。借助现有为线性响应设计的高性能预测模型，我们分析了一种通用投影方法，可将任何线性响应回归模型转换为适用于圆响应的模型。当随机森林作为该投影过程中的基础模型时，我们利用随机森林的袋外机制消除了在构建预测集时对单独校正样本的需求。在合成数据集和真实数据集上，与两种现有替代模型生成的拆分共形预测集相比，所得到的投影随机森林模型生成的袋外共形预测集效率更高，中位弧长更短。