因果图中的调整标准：一个数学的视角
Adjustment Criteria in Causal Diagrams: An Algorithmic Perspective
摘要：
识别和控制偏差是经验科学中的一个关键问题。因果图理论提供了决定是否以及如何通过协变量调整从观察（非实验）数据中识别因果效应的图形标准。在这里，我们证明现有的以及新的标准之间的等价调整，我们提供了一个新的简化，但仍然等效的概念D-分离。这些导致有效的算法在因果图分析中的两个重要任务：（1）列出最小的协变量调整（多项式延迟）;和（2）确定涉及偏置路径的子图（在线性时间）。我们的结果改进了现有的指数时间解决方案，这些问题，使用户能够评估协变量调整的影响图与几十到几百个变量的交互式实时的。
英文摘要：
Identifying and controlling bias is a key problem in empirical sciences. Causal diagram theory provides graphical criteria for deciding whether and how causal effects can be identified from observed (nonexperimental) data by covariate adjustment. Here we prove equivalences between existing as well as new criteria for adjustment and we provide a new simplified but still equivalent notion of d-separation. These lead to efficient algorithms for two important tasks in causal diagram analysis: (1) listing minimal covariate adjustments (with polynomial delay); and (2) identifying the subdiagram involved in biasing paths (in linear time). Our results improve upon existing exponential-time solutions for these problems, enabling users to assess the effects of covariate adjustment on diagrams with tens to hundreds of variables interactively in real time.
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