NESTED MARKOV PROPERTIES FOR ACYCLIC DIRECTED MIXED GRAPHS
NESTED MARKOV PROPERTIES FOR ACYCLIC DIRECTED MIXED GRAPHS
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DOI：
10.1214/22-aos2253
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发表时间：
2023-02-01
影响因子：
4.5
通讯作者：
Shpitser, Ilya
中科院分区：
文献类型：
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作者：
Richardson, Thomas S.;Evans, Robin J.;Shpitser, Ilya
与有向无环图（DAG）相关联的条件独立模型可以至少以三种不同的方式来表征：通过因子分解、全局马尔可夫性质（由d-分离准则给出）和局部马尔可夫性质。DAG模型的边际也意味着不是条件独立的等式约束;众所周知的？维尔玛约束？就是一个例子。这种类型的约束用于测试边缘，并通过变量消除在计算上有效的边缘化方案。我们表明，平等的约束，如？维尔玛约束？可以被看作是通过固定操作从联合分布获得的内核对象中的条件独立性，该固定操作概括了条件和边缘化。我们使用这些约束来定义，通过有序的本地和全球马尔可夫性质，和一个因子分解，与无环有向混合图（ADMGs）的图形模型。我们证明了DAG模型的边际分布存在于这个模型中，并且由Tian给出的一组这些约束提供了模型的另一种定义。最后，我们表明，固定操作用于定义模型导致一个特别简单的表征可识别的因果效应在隐变量因果DAG模型。
Conditional independence models associated with directed acyclic graphs (DAGs) may be characterized in at least three different ways: via a factorization, the global Markov property (given by the d-separation crite-rion), and the local Markov property. Marginals of DAG models also imply equality constraints that are not conditional independences; the well-known ???Verma constraint??? is an example. Constraints of this type are used for testing edges, and in a computationally efficient marginalization scheme via variable elimination. We show that equality constraints like the ???Verma constraint??? can be viewed as conditional independences in kernel objects obtained from joint distributions via a fixing operation that generalizes conditioning and marginalization. We use these constraints to define, via ordered local and global Markov properties, and a factorization, a graphical model associated with acyclic directed mixed graphs (ADMGs). We prove that marginal distri-butions of DAG models lie in this model, and that a set of these constraints given by Tian provides an alternative definition of the model. Finally, we show that the fixing operation used to define the model leads to a particularly simple characterization of identifiable causal effects in hidden variable causal DAG models.