利用层级结构优化预测区间，提升置信区间效率。
Conformal Prediction for Hierarchical Data
- 在分割共形预测中引入投影步骤，利用数据层级关系压缩预测范围。
- 在联合覆盖与分量覆盖两种场景下，均实现更小的预测区域。
- 适用于具有层次结构的多变量预测任务，如时间序列汇总预测。
我们研究多变量数据的共形预测，重点关注组件间存在线性关系的层级数据。直观上，层级结构可用于在相同覆盖率下缩小预测区间。为此，在分割共形预测（SCP）流程中加入投影（又称校正）步骤，并证明所得预测区间确实更小。该结论在经典联合覆盖目标下成立，也在更具挑战性的分量覆盖任务中得到验证。相关策略与分析结合了SCP与预测校正的文献。我们在不同规模的层级结构上对模拟数据进行了实验，验证了理论结果。
原文摘要 · Abstract (English)
We consider conformal prediction for multivariate data and focus on hierarchical data, where some components are linear combinations of others. Intuitively, the hierarchical structure can be leveraged to reduce the size of prediction regions for the same coverage level. We implement this intuition by including a projection step (also called a reconciliation step) in the split conformal prediction [SCP] procedure, and prove that the resulting prediction regions are indeed globally smaller. We do so both under the classic objective of joint coverage and under a new and challenging task: component-wise coverage, for which efficiency results are more difficult to obtain. The associated strategies and their analyses are based both on the literature of SCP and of forecast reconciliation, which we connect. We also illustrate the theoretical findings, for different scales of hierarchies on simulated data.
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