Unifying Markov properties for graphical models
Unifying Markov properties for graphical models
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统一图形模型的马尔可夫属性
DOI：
10.1214/17-aos1618
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Kayvan Sadeghi
中科院分区：
文献类型：
--
作者：
S. Lauritzen;Kayvan Sadeghi
已经提出了几种具有不同条件独立性解释的图-也称为马尔可夫性质-并在图形模型中使用。在本文中，我们通过引入一类具有四种边-线、箭头、弧和虚线--的图和一个单一的分离准则来统一这些马尔可夫性质。我们证明了当考虑图的合适的子类时，由这类定义的独立结构专用于前面定义的每一种情况。此外，我们还定义了链混合图的子类的两两马氏性，它包括具有LWF解释的链图以及汇总图(以及由此而来的祖先图)。我们证明了这种两两马氏性与组成类独立模型的全局马氏性是等价的。
Several types of graphs with different conditional independence interpretations --- also known as Markov properties --- have been proposed and used in graphical models. In this paper we unify these Markov properties by introducing a class of graphs with four types of edges --- lines, arrows, arcs, and dotted lines --- and a single separation criterion. We show that independence structures defined by this class specialize to each of the previously defined cases, when suitable subclasses of graphs are considered. In addition, we define a pairwise Markov property for the subclass of chain mixed graphs which includes chain graphs with the LWF interpretation, as well as summary graphs (and consequently ancestral graphs). We prove the equivalence of this pairwise Markov property to the global Markov property for compositional graphoid independence models.