关于无环有向混合图的统计与因果模型
On statistical and causal models associated with acyclic directed mixed graphs
AI总结：
本文综述无环有向混合图（ADMGs）的多种解释，论证噪声扩展（NE）模型应作为默认解释，因其具备完备性且不依赖特定潜变量假设，并批判了常见的潜变量DAG解释。
摘要：
统计学中的因果模型通常使用无环有向混合图（ADMGs）来描述，这类图包含有向边和双向边，且不存在有向环。本文综述了ADMGs的各种解释，讨论了它们在不同ADMGs子类中的关系，并论证其中一种解释——噪声扩展（NE）模型——应作为默认解释。我们支持NE模型的依据基于两点观察。第一，在ADMGs的一个称为无混杂图的子类中（该子类保留了有向无环图和双向图的大部分优良性质），NE模型与包括全局马尔可夫模型和嵌套马尔可夫模型在内的许多其他解释等价。第二，任意ADMG的NE模型恰好是该图所有无混杂扩展的NE模型的并集。这一性质被称为完备性，因为它表明该模型不依赖于任何特定的潜变量解释。在证明NE模型是嵌套马尔可夫的过程中，我们还发展了一种基于ADMG的因果理论。最后，我们将NE模型与文献中常用的将ADMGs解释为带潜变量的有向无环图（DAGs）这一密切相关但不同的解释进行比较。我们认为，“潜变量DAG”解释在数学上是不必要的，它引入了模糊的本体论假设，并阻碍实践者审慎考虑重要的结构假设。
英文摘要：
Causal models in statistics are often described using acyclic directed mixed graphs (ADMGs), which contain directed and bidirected edges and no directed cycles. This article surveys various interpretations of ADMGs, discusses their relations in different sub-classes of ADMGs, and argues that one of them -- the noise expansion (NE) model -- should be used as the default interpretation. Our endorsement of the NE model is based on two observations. First, in a subclass of ADMGs called unconfounded graphs (which retain most of the good properties of directed acyclic graphs and bidirected graphs), the NE model is equivalent to many other interpretations including the global Markov and nested Markov models. Second, the NE model for an arbitrary ADMG is exactly the union of that for all unconfounded expansions of that graph. This property is referred to as completeness, as it shows that the model does not commit to any specific latent variable explanation. In proving that the NE model is nested Markov, we also develop an ADMG-based theory for causality. Finally, we compare the NE model with the closely related but different interpretation of ADMGs as directed acyclic graphs (DAGs) with latent variables that is commonly used in the literature. We argue that the "latent DAG" interpretation is mathematically unnecessary, makes obscure ontological assumptions, and discourages practitioners from deliberating over important structural assumptions.
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