Split conformal prediction techniques are applied to regression problems with circular responses by introducing a suitable conformity score, leading to prediction sets with adaptive arc length and finite-sample coverage guarantees for any circular predictive model under exchangeable data. 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 serve as basis models in this projection procedure, we harness the out-of-bag dynamics to eliminate the necessity for a separate calibration sample in the construction of prediction sets. For synthetic and real datasets the resulting projected random forests model produces more efficient out-of-bag conformal prediction sets, with shorter median arc length, when compared to the split conformal prediction sets generated by two existing alternative models.

翻译：通过引入合适的符合度评分，将分割保形预测技术应用于具有圆形响应的回归问题，从而为任何圆形预测模型在可交换数据下生成具有自适应弧长和有限样本覆盖保证的预测集。利用现有针对线性响应设计的预测模型的高性能，我们分析了一种通用投影方法，该方法可将任何线性响应回归模型转换为适用于圆形响应的模型。当随机森林作为该投影方法的基础模型时，我们利用袋外动态特性消除了构建预测集时对单独校准样本的需求。在合成和真实数据集上，与两种现有替代模型生成的分割保形预测集相比，所得投影随机森林模型能产生更高效的袋外保形预测集，其中位弧长更短。