在因果信息不完整时，仍能有效估算因果概率的上下界。
Bounding Probabilities of Causation with Partial Causal Diagrams
- 用优化框架整合部分因果结构与统计信息作为约束
- 无需完整因果图即可得到更紧且严谨的边界
- 适合因果推断不完全但有部分知识的实际场景
因果概率是个人层面解释与决策的基础，但本质上是反事实的，在一般情况下无法从数据中唯一确定。现有方法要么忽略协变量，要么需要完整的因果图，或依赖严格的二值设定，限制了实际应用。在真实场景中，因果信息往往部分已知但非无关。本文提出一种使用部分因果信息来界定因果概率的通用框架。通过将可用的结构或统计信息系统地转化为优化问题中的约束，可获得更紧且形式上有效的边界，而无需完全可识别性。该方法扩展了因果概率在因果知识不完整但仍有信息的现实情境下的适用性。
原文摘要 · Abstract (English)
Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates, require complete causal graphs, or rely on restrictive binary settings, limiting their practical use. In real-world applications, causal information is often partial but nontrivial. This paper proposes a general framework for bounding probabilities of causation using partial causal information. We show how the available structural or statistical information can be systematically incorporated as constraints in a optimization programming formulation, yielding tighter and formally valid bounds without full identifiability. This approach extends the applicability of probabilities of causation to realistic settings where causal knowledge is incomplete but informative.
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