将因果知识融入多值因果概率，显著缩小估计区间。
General Probabilities of Causation with Causal Knowledge
- 利用协变量和中介变量中的因果信息优化多值因果概率边界
- 理论推导出比现有方法更紧的边界，仿真验证效果提升
- 适合从事因果推断、政策评估的研究者参考
因果概率（PoCs）刻画无法直接观测的个体因果效应，通常仅能部分识别。Tian 和 Pearl 首次为二值 PoC（包括必要性概率 PN、充分性概率 PS 以及必要且充分概率 PNS）推导出理论最优边界。Mueller 等人通过引入协变量和中介变量中的因果信息，进一步收紧了二值 PNS 的边界。近期，Li 和 Pearl 以及 Shu 等人将 PoCs 扩展至多值场景并推导出相应理论边界。本文在此基础上，研究是否可借助更多因果知识进一步收紧多值 PoCs 的边界。结果表明，通过融合协变量与中介变量中的因果信息，可导出更紧的多值 PoCs 边界。我们通过简单示例说明理论结果，并通过模拟实验验证所提边界优于现有非二值边界。
原文摘要 · Abstract (English)
Probabilities of causation (PoCs) characterize individual causal responses that cannot be directly observed and therefore generally require partial identification. Tian and Pearl first derived theoretically sharp bounds for binary PoCs, including the probability of necessity (PN), the probability of sufficiency (PS), and the probability of necessity and sufficiency (PNS). Mueller et al. subsequently tightened the bounds for binary PNS by incorporating causal information encoded in covariates and mediators. More recently, Li and Pearl, as well as Shu et al., extended PoCs to multivalued settings and derived corresponding theoretical bounds. These developments naturally raise the question of whether additional causal knowledge can further tighten the bounds in multivalued settings. This paper addresses this question by deriving tighter bounds for multivalued PoCs through the incorporation of causal information encoded in covariates and mediators. We illustrate the theoretical results with toy examples, while simulation studies further demonstrate that the proposed bounds are tighter than existing nonbinary bounds.
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