发表机构
Imperial College London（帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究尖锐因果界在跨环境组合时失效的条件，发现仅当绝对选择界一致时组合成立，并给出计算复杂度与扰动证书，区分局部尖锐与联合可达性。
AI 中文摘要
两个潜在结果均值的尖锐界并不必然组合成其差值的尖锐界。我们精确刻画了在共享联合潜在结果定律的环境中，组合何时得到保证。对于二元处理和二元结果，固定严格的选择概率界和内部的处理倾向。当且仅当各环境间的绝对选择界一致时，从完整模型的尖锐均值区间相减得到每个兼容观测定律的尖锐平均处理效应界。在此对齐条件下，完整的均值区域是矩形的；其端点和达到的因果模型需要 $K$ 个环境下的 $O(K)$ 次算术运算。对于任何不匹配，在指定倾向下，失败发生在正观测表的相对开集上，并在小的联合漂移下持续存在。我们给出可计算的扰动证书和一个精确族，其间隙在失配中是一阶的。一个独立的有限混杂族展示了丢失的联合信息何时改变已识别的因果符号。这些结果区分了局部边际尖锐性与组合环境后的联合可达性。
英文摘要
Sharp bounds on two potential-outcome means need not combine into sharp bounds on their difference. We characterize exactly when composition is guaranteed across environments sharing a joint potential-outcome law. For binary treatment and outcome, fix strict selection-probability bounds and interior treatment propensities. Subtracting the full model's sharp mean intervals gives sharp average-treatment-effect bounds for every compatible observed law if and only if the absolute selection bounds coincide across environments. Under this alignment, the complete mean region is rectangular; its endpoints and attaining causal models require $O(K)$ arithmetic operations for $K$ environments. For every mismatch, failure occurs on a relatively open set of positive observed tables at the prescribed propensities and persists under small joint drift. We give computable perturbation certificates and an exact family whose gap is first order in the mismatch. A separate finite-confounding family shows when the lost joint information changes an identified causal sign. These results distinguish local marginal sharpness from joint attainability after combining environments.
Comments32 pages, 1 figure. Includes appendices
