A Characterization of Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables
A Characterization of Markov Equivalence Classes for Directed Acyclic Graphs with Latent Variables
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含潜变量有向无环图马尔可夫等价类的刻画
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发表时间：
2007
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通讯作者：
Jiji Zhang
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作者：
Jiji Zhang
不同的有向无环图（DAG）可能是马尔可夫等价的，因为它们在观测变量之间具有相同的条件独立关系。Meek（1995）通过提出一组方向规则来表征DAG的马尔可夫等价类（没有潜在变量），该方向规则可以正确地识别马尔可夫等价类中所有DAG共享的所有箭头方向，给定该类的成员。对于具有潜在变量的DAG模型，最大祖先图（MAG）提供了一种简洁的表示，便于模型搜索。早期的工作（阿里等人，2005年）已经确定了一套方向规则，足以构建所有箭头共同的马尔可夫等价类的MAG。在本文中，我们提供了额外的规则足以构造所有共同的尾巴。我们最终与一组定位规则的声音和完整的识别跨马尔可夫等价类的MAG，这是特别有用的因果推理的共性。
Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Meek (1995) characterizes Markov equivalence classes for DAGs (with no latent variables) by presenting a set of orientation rules that can correctly identify all arrow orientations shared by all DAGs in a Markov equivalence class, given a member of that class. For DAG models with latent variables, maximal ancestral graphs (MAGs) provide a neat representation that facilitates model search. Earlier work (Ali et al. 2005) has identified a set of orientation rules sufficient to construct all arrowheads common to a Markov equivalence class of MAGs. In this paper, we provide extra rules sufficient to construct all common tails as well. We end up with a set of orientation rules sound and complete for identifying commonalities across a Markov equivalence class of MAGs, which is particularly useful for causal inference.