无需完整因果图，用线性规划推导反事实的紧致边界。
Partial Identification under Causal Orders by Linear Programming
- 基于反事实查询自身推导变量拓扑序，构建可解线性规划
- 对任意反事实及嵌套反事实均可给出紧致边界
- 适用于缺乏完整因果知识的场景，适合因果推断研究者
非参数化（部分）识别反事实问题通常依赖完整的因果图。针对领域知识不全的情形，本文提出利用查询本身隐含的结构假设。我们证明任何反事实询问都会诱导出相关变量的大部分偏序关系，进而实现查询参数化，将识别问题转化为线性规划。该方法可对任意反事实及嵌套反事实查询进行边界估计。本工作是Tian与Pearl（2000）经典概率因果框架的推广。我们通过构造与观测数据和查询诱导顺序兼容的结构因果模型，证明了边界的紧致性。为验证方法的通用性与实用性，我们在文献中的多个案例上重检，展示了即使无输入因果图，所推边界仍能提供有效洞见。
原文摘要 · Abstract (English)
Non-parametric (partial) identification of counterfactual queries typically relies on a fully specified causal graph. Motivated by settings with incomplete domain knowledge, we challenge this requirement by leveraging structural assumptions that are inherently implied by the query itself. We show that any counterfactual inquiry induces a, mostly partial, topological ordering over relevant variables, which, in turn, enables an explicit query parametrisation reducing the identification task to a linear program. This allows bounding arbitrary counterfactual and nested counterfactual queries. Our work can be viewed as a generalisation of the classical bounding framework of Tian and Pearl (2000), originally developed for probabilities of causation. We also prove the \emph{tightness} of our bounds by constructing structural causal models that attain the bounds whilst being compatible with both the observed data and the query-implied order. To assess both the generality and practical utility of the proposed bounding procedure, we revisit several case studies from the literature, demonstrating how the derived bounds can be used to yield informative insights even in the absence of an input causal graph.
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