将随机森林与共形预测结合，高效生成圆数据的预测区间。
Projected random forests and conformal prediction of circular data
- 通过投影法将线性回归模型转为圆数据适用模型。
- 无需单独校准集，用袋外样本直接生成预测集，中位弧长更短。
- 适合需要精准圆数据预测的场景，如方向或角度建模。
我们将在圆数据上的回归问题中应用共形预测技术，为任意基于数据可交换性的圆响应预测模型提供具有自适应弧长和有限样本覆盖保证的预测集。通过利用针对线性响应设计的高性能预测模型，我们分析了一种通用的投影方法，可将任何线性响应回归模型转换为适用于圆响应的模型。当在该投影过程中使用随机森林作为基础模型时，我们借助随机森林的袋外机制，消除了构建预测集所需的独立校准样本。在合成数据和真实数据集上的实验表明，所得的投影随机森林模型生成的袋外共形预测集比两种现有替代模型生成的分割共形预测集更具效率，中位弧长更短。
原文摘要 · Abstract (English)
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.
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