Accuracy Limits of Causal Trees for Individualized Treatment Effects
因果树估计个体化处理效应的精度极限AI 解读 ↓
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因果树估计个体化处理效应的精度极限
- 研究问题
- 使用常见递归分割规则的因果树，能否在整个协变量空间准确估计处理效应，样本分割是否能够消除局部估计误差？
- 方法与思路
- 作者对自适应因果树建立估计精度下界，覆盖有无样本分割的常见分割准则，并分析不平衡分割如何形成小叶节点和高方差。
- 材料陈述的贡献
- 摘要称即使随机分配且效应恒定，所研究因果树的一致范数误差也可能任意缓慢下降；平均平方误差较小仍可能掩盖局部失准。
- 阅读关注点
- 应核对下界适用的树类、分割及停止规则、概率量词和误差度量，并区分单棵因果树结果与森林或其他集成方法的保证。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收；摘要未列出完整条件，不能把该精度限制推广到所有因果森林。
原文摘要
Recursive decision trees are widely used to estimate heterogeneous causal treatment effects in experimental and observational studies. These methods are typically implemented using CART-type recursive partitioning, with splitting criteria designed to identify variation in treatment effects across covariate-defined subgroups. We study causal tree estimators based on adaptive recursive partitioning and establish lower bounds on their estimation accuracy. The class we analyze includes versions with and without sample splitting, based on common treatment effect and squared-error splitting criteria. Even in a constant-effect benchmark with randomized treatment assignment, causal trees constructed via standard CART-type splitting rules can have uniform-norm errors that decrease more slowly than any power of the sample size. The underlying mechanism is that greedy recursive partitioning selects highly imbalanced splits with nonvanishing probability, producing terminal nodes containing very few observations and leading to large estimation variance. We further show that sample splitting, often called ``honesty,'' does not remove this limitation. As a consequence, causal tree estimators may converge arbitrarily slowly uniformly over the covariate space. At the same time, these estimators can have small integrated mean squared error, showing that average accuracy can mask local inaccuracy. Our results also clarify the role of balanced partition assumptions in existing theoretical guarantees for causal forests and related ensemble methods.