AI 中文总结
PATH通过自回归树层次结构建模区间的嵌套关系，在PATHBench数据集上相比24种基线方法，以0.9144的平均覆盖水平实现了0.1473的最低平均归一化区间长度，为表格数据的紧凑区间预测提供了有效方案。
AI 中文摘要
区间预测旨在达到目标覆盖水平，同时生成尽可能短的区间。许多共形回归流程首先预测不确定性代理，然后通过校准或选择将其转换为区间。这种分离支持覆盖校准，但事后规则在很大程度上决定了最终区间，且未充分利用学习到的输出分布。我们观察到，生成的区间具有固有的层次几何结构：区间可递归细化为嵌套子区间，二叉树自然地表示这种结构。我们将该层次结构形式化为下一个区间预测，并提出PATH，该方法学习概率质量如何从每个区间流向其下一个嵌套子区间。PATH预测基础叶分布，并使用自回归解码器细化分支概率。将分布与区间层次结构匹配使学习与提取相一致：PATH在相邻输出区间上累积概率，并返回达到选定质量的最短连续范围。我们在包含56个OpenML回归数据集的PATHBench上，将PATH与24种区间预测基线进行比较。PATH大幅缩短了生成的区间，实现了最低的平均归一化长度0.1473，同时保持了0.9144的平均覆盖水平。这些结果确立了层次输出建模是表格数据紧凑区间预测的有效方法。代码可在该httpsURL公开获取。
英文摘要
Interval prediction aims to achieve a target coverage level while producing intervals that are as short as possible. Many conformal regression pipelines first predict an uncertainty surrogate and then convert it into an interval through calibration or selection. This separation supports coverage calibration, but post hoc rules largely determine the final interval and do not fully use the learned output distribution. We observe that the resulting intervals have inherently hierarchical geometry: an interval can be recursively refined into nested subintervals, and binary trees naturally represent this structure. We formulate this hierarchy as next-interval prediction and propose PATH, which learns how probability mass flows from each interval to its next nested subintervals. PATH predicts a base leaf distribution and uses an autoregressive decoder to refine branch probabilities. Matching the distribution to the interval hierarchy aligns learning with extraction: PATH accumulates probability over adjacent output intervals and returns the shortest contiguous range reaching a selected mass. We compare PATH with 24 baselines for interval prediction on PATHBench, comprising 56 OpenML regression datasets. PATH substantially shortens the resulting intervals, achieving the lowest mean normalized length, 0.1473, while maintaining mean coverage of 0.9144. These results establish hierarchical output modeling as an effective approach for compact interval prediction on tabular data. Code is publicly available at https://github.com/pxcai/PATH.
