标题： 跨世界假设与个体处理效应预测区间的修正 显示英文标题

标题： Cross-World Assumption and Refining Prediction Intervals for Individual Treatment Effects

摘要： 虽然平均处理效应（ATE）和条件平均处理效应（CATE）提供了有价值的总体和子群体水平的总结，但它们无法捕捉个体层面的不确定性。 对于高风险决策，个体处理效应（ITE）估计必须伴随有效的预测区间，这些区间能够反映异质性和个体特定的不确定性。 然而，ITE的根本不可识别性限制了得出精确且可靠的个体层面不确定性估计的能力。 为了解决这一挑战，我们研究了一个交叉世界相关参数$ \rho(x) = cor(Y(1), Y(0) | X = x) $的作用，该参数描述了在给定协变量的情况下，潜在结果之间的依赖关系，在具有独立同分布单位的Neyman-Rubin超总体模型中。 尽管$ \rho $在本质上是不可识别的，但我们认为在大多数现实应用中，可以通过领域专家知识施加合理且可解释的界限。 给定$\rho$，我们设计了ITE的预测区间，实现了更稳定和准确的覆盖率，且区间宽度显著缩短；通常小于竞争方法的1/3。 所得区间满足覆盖率保证$P\big(Y(1) - Y(0) \in C_{ITE}(X)\big) \geq 1 - \alpha$，并在正态假设下渐近最优。 我们提供了强有力的理论和实证论据，表明交叉世界假设可以使个体不确定性量化既具有实际信息价值，又具有统计有效性。 显示英文摘要

摘要： While average treatment effects (ATE) and conditional average treatment effects (CATE) provide valuable population- and subgroup-level summaries, they fail to capture uncertainty at the individual level. For high-stakes decision-making, individual treatment effect (ITE) estimates must be accompanied by valid prediction intervals that reflect heterogeneity and unit-specific uncertainty. However, the fundamental unidentifiability of ITEs limits the ability to derive precise and reliable individual-level uncertainty estimates. To address this challenge, we investigate the role of a cross-world correlation parameter, $ \rho(x) = cor(Y(1), Y(0) | X = x) $, which describes the dependence between potential outcomes, given covariates, in the Neyman-Rubin super-population model with i.i.d. units. Although $ \rho $ is fundamentally unidentifiable, we argue that in most real-world applications, it is possible to impose reasonable and interpretable bounds informed by domain-expert knowledge. Given $\rho$, we design prediction intervals for ITE, achieving more stable and accurate coverage with substantially shorter widths; often less than 1/3 of those from competing methods. The resulting intervals satisfy coverage guarantees $P\big(Y(1) - Y(0) \in C_{ITE}(X)\big) \geq 1 - \alpha$ and are asymptotically optimal under Gaussian assumptions. We provide strong theoretical and empirical arguments that cross-world assumptions can make individual uncertainty quantification both practically informative and statistically valid.