AI 中文总结
针对分组数据预测中标准分层共形预测无法利用少量初始观测的问题，提出广义分层共形预测（GHCP）方法，通过分配随机参考组大小恢复对称性并提升非一致性分数，经模拟和美国社区调查数据集验证性能。
AI 中文摘要
许多预测问题源于分组收集的数据。在此设定下，分层共形预测（HCP，Lee等人，2026）在分层可交换性下为来自未见组的新观测提供无分布预测集。然而在许多应用中，仅在已收集到目标组的少量观测后才进行预测。标准HCP无法利用这些观测，因为其所需的对称性条件在此设定下不成立。同时，初始样本可能仍过小，无法对测试组应用标准共形预测以获取有效信息。我们为此设定开发预测推理方法。所提方法广义分层共形预测（GHCP）通过为测试组分配随机“捐赠”的参考组大小，恢复共形推理所需的相关对称性；GHCP还利用初始测试组观测，提升该组内预测的非一致性分数质量。为提高效率，我们引入限制合格捐赠者集合的变体。我们通过模拟和美国社区调查（American Community Survey）数据集上的示例，展示所提方法的性能。
英文摘要
Many prediction problems arise with data collected in groups. In this setting, hierarchical conformal prediction (HCP) (Lee et al., 2026) provides distribution-free prediction sets for a new observation from a previously unseen group under hierarchical exchangeability. In many applications, however, prediction is conducted only after a few observations from the group of interest have already been collected. Standard HCP cannot leverage these observations, as its required symmetry conditions do not hold in this setting. At the same time, the initial sample may still be too small for standard conformal prediction applied within the test group to be informative. We develop predictive inference methods for this setting. Our proposed method, Generalized HCP (GHCP), restores the relevant symmetry needed for conformal inference by assigning the test group a randomly "donated" reference group size. GHCP further leverages the initial test group observations to improve the quality of the nonconformity scores for prediction within that group. To improve efficiency, we introduce a variant that restricts the set of eligible donors. We demonstrate the performance of the proposed method through simulations and an illustration on the American Community Survey dataset.
Comments44 pages, 13 figures. Code available at https://github.com/soham-penn/hierarchical_CP
