有向无圈图的介入Markov等价类的刻画与贪婪学习
Characterization and Greedy Learning of Interventional Markov Equivalence Classes of Directed Acyclic Graphs
摘要：
有向无环图（DAG）编码相同的马尔可夫性，即相同的条件独立关系的多变量观测分布的调查，有着悠久的传统，存在许多算法的模型选择和结构学习的马尔可夫等价类。在本文中，我们扩展了马尔可夫等价的DAG的概念的情况下，所产生的多个干预实验的干预分布。我们发现，在合理的假设下，干预实验，干预马尔可夫等价定义了一个更精细的划分的DAG比观察马尔可夫等价，从而提高了因果模型的可识别性。我们给出了一个图论标准的两个DAG是马尔可夫等价的干预下，并表明，每个干预马尔可夫等价类可以，类似于观察的情况下，唯一表示的链图称为干预本质图（也称为CPDAG在观察的情况下）。这些是用于从介入数据中获得结构学习的贪婪等价搜索算法的推广的关键见解。这种新的算法进行了评估，在模拟研究。
英文摘要：
The investigation of directed acyclic graphs (DAGs) encoding the same Markov property, that is the same conditional independence relations of multivariate observational distributions, has a long tradition; many algorithms exist for model selection and structure learning in Markov equivalence classes. In this paper, we extend the notion of Markov equivalence of DAGs to the case of interventional distributions arising from multiple intervention experiments. We show that under reasonable assumptions on the intervention experiments, interventional Markov equivalence defines a finer partitioning of DAGs than observational Markov equivalence and hence improves the identifiability of causal models. We give a graph theoretic criterion for two DAGs being Markov equivalent under interventions and show that each interventional Markov equivalence class can, analogously to the observational case, be uniquely represented by a chain graph called interventional essential graph (also known as CPDAG in the observational case). These are key insights for deriving a generalization of the Greedy Equivalence Search algorithm aimed at structure learning from interventional data. This new algorithm is evaluated in a simulation study.
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