Uncertainty quantification for individual treatment effects (ITEs) is a daunting challenge in causal inference. Motivated by recent advances in conformal prediction, several works aim to construct distribution-free prediction sets for ITEs with desired coverage under standard assumptions such as strong ignorability and overlap. In this paper, we show that such goals are fundamentally unattainable in the presence of continuous covariates. Specifically, we establish finite-sample and asymptotic impossibility results demonstrating that any distribution-free prediction set achieving desired coverage for ITEs must be trivial, in the sense that it has infinite expected length. Our analysis relies on a connection between ITE inference and the hardness of conditional independence testing, and highlights the intrinsic limitations imposed by the missing data nature of causal inference. These results provide a new perspective on existing methods, clarifying that their apparent success necessarily relies on additional structural assumptions beyond standard causal assumptions.

翻译：个体治疗效果的不确定性量化是因果推断中的一项艰巨挑战。受近期共形预测进展的启发，多项研究旨在构建个体治疗效果的分布自由预测集，使其在强可忽略性与重叠性等标准假设下达到期望覆盖率。本文证明，当存在连续协变量时，这类目标本质上不可实现。具体而言，我们建立了有限样本与渐近不可能性结果，表明任何在个体治疗效果上达到期望覆盖率的分布自由预测集必然是平凡的——即其期望长度无限。该分析基于个体治疗效果推断与条件独立性检验难度之间的关联，揭示了因果推断中缺失数据本质所施加的内在限制。这些结果对现有方法提供了全新视角，阐明其表面成功必然依赖标准因果假设之外的结构性约束。