发表机构
Faculty of Health Data Science, Juntendo University（顺天堂大学健康数据科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对二元分类树的选择性推断问题，提出基于Gini CART的有限样本条件检验，通过均匀标签纤维和并行蒙特卡洛构造p值，在模拟中验证了其保守性和对较大风险差异的检测功效。
AI 中文摘要
二元分类树使用与后续评估组间差异相同的结果来选择子组。我们针对由确定性Gini CART选择的父节点，开发了共同成功概率的有限样本条件检验。该构造保留所有符合条件的切分点，并以所选分割、其祖先路径、父节点成功总数及外部结果为条件。由此产生的均匀标签纤维给出了精确的计数分布，而可逆的并行蒙特卡洛构造在任意预设的有限运行预算下，产生超均匀的包含性p值和精确均匀的平局随机化p值。在两子节点恒定风险模型中，所选计数定律是一个指数族，其信息量等于其条件计数方差。我们将信息损失与计算限制分开，并展示了一个在单标签交换下不连通的所选纤维。模拟使用200或400个观测值、十个独立或相关预测变量以及深度为三的树，显示包含性检验是保守的，且对大的风险差异具有非平凡的功效。在400个观测值且生成风险差异为0.4时，以到达预设第三层目标为条件的随机化拒绝率为51%至71%，而选择后拒绝发生在11%至21%的数据集中。较小的信号仍然难以检测，且计算量增加五倍的代表性情况仅带来微小的功效提升。该保证涉及父节点同质性，即两个恒定子节点风险的相等性，并不涵盖异质区域平均值的相等性。
英文摘要
Binary classification trees select subgroups using the same outcomes later used to assess their differences. We develop finite-sample conditional tests of a common success probability within a parent selected by deterministic Gini CART. The construction retains all eligible cutpoints and conditions on the selected split, its ancestor path, the parent success total, and outside outcomes. The resulting uniform label fiber gives an exact count distribution, while a reversible parallel Monte Carlo construction yields super-uniform inclusive and exactly uniform tie-randomized p-values for any prespecified finite run budget. Within a two-child constant-risk model, the selected count law is an exponential family with information equal to its conditional count variance. We separate information loss from computational limitations and exhibit a selected fiber disconnected under single-label swaps. Simulations with 200 or 400 observations, ten independent or correlated predictors, and trees of depth three show conservative inclusive tests and nontrivial power for large risk differences. At 400 observations and a generating risk difference of 0.4, randomized rejection conditional on reaching the prespecified third-level target is 51--71\%, while selection followed by rejection occurs in 11--21\% of datasets. Smaller signals remain difficult to detect, and a representative fivefold increase in computation gives little power improvement. The guarantee concerns parent homogeneity, or equality of two constant child risks, and does not cover equality of heterogeneous regional averages.
