Generalized Do-Calculus with Testable Causal Assumptions
Generalized Do-Calculus with Testable Causal Assumptions
复制标题
具有可测试因果假设的广义 Do-Calculus
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
Jiji Zhang
中科院分区：
文献类型：
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作者：
Jiji Zhang
因果推理的主要目标涉及系统在某些干预下会发生什么。具体来说，我们通常对估计某些随机变量的概率分布感兴趣，这些随机变量是由于强制其他一些变量取某些值而产生的。著名的 do-calculus（Pearl 1995）给出了一组规则，用于根据（可估计的）干预前概率来管理此类干预后概率的识别，假设有一个代表潜在因果结构的有向无环图（DAG）。然而，鉴于干预前的观察数据，DAG 因果结构很少是完全可测试的，因为许多竞争的 DAG 结构与数据同样兼容。在本文中，我们将 do-calculus 扩展到涵盖可用因果信息总结在所谓的部分祖先图（PAG）中的情况，PAG 表示 DAG 结构的等价类。 PAG 编码的因果假设明显弱于成熟的 DAG 因果结构编码的因果假设，并且原则上可以通过观察到的条件独立关系进行完全测试。
A primary object of causal reasoning concerns what would happen to a system under certain interventions. Specifically, we are often interested in estimating the probability distribution of some random variables that would result from forcing some other variables to take certain values. The renowned do-calculus (Pearl 1995) gives a set of rules that govern the identification of such post-intervention probabilities in terms of (estimable) pre-intervention probabilities, assuming available a directed acyclic graph (DAG) that represents the underlying causal structure. However, a DAG causal structure is seldom fully testable given preintervention, observational data, since many competing DAG structures are equally compatible with the data. In this paper we extend the do-calculus to cover cases where the available causal information is summarized in a so-called partial ancestral graph (PAG) that represents an equivalence class of DAG structures. The causal assumptions encoded by a PAG are significantly weaker than those encoded by a full-blown DAG causal structure, and are in principle fully testable by observed conditional independence relations.