结合因果知识的一般因果概率
General Probabilities of Causation with Causal Knowledge
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中文总结 AI 辅助
本文针对多值因果概率边界可进一步收紧的问题，整合协变量与中介变量的因果信息推导更紧边界，经示例和模拟验证其边界优于现有非二元边界。
中文摘要 AI 辅助
因果概率（PoCs）表征无法直接观测的个体因果响应，通常需要部分识别。Tian和Pearl首次从理论上推导了二元PoCs的严格边界，包括必要性概率（PN）、充分性概率（PS）以及必要性与充分性概率（PNS）。随后Mueller等人通过整合协变量和中介变量中编码的因果信息，收紧了二元PNS的边界。近期Li和Pearl以及Shu等人将PoCs扩展到多值设置并推导了相应的理论边界。这些进展自然引出一个问题：在多值设置中，额外的因果知识能否进一步收紧边界？本文通过整合协变量和中介变量中编码的因果信息，推导了多值PoCs的更紧边界。我们用示例说明理论结果，模拟研究进一步表明，所提出的边界比现有的非二元边界更紧。
英文摘要
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.
