循环导导混合图的替代Markov和构造属性 (Alternative Markov and Causal Properties for Acyclic Directed Mixed Graphs)

We extend Andersson-Madigan-Perlman chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, and ordered local and pairwise Markov properties for the new models. We show the equivalence of these properties for strictly positive probability distributions. We also show that when the random variables are continuous, the new models can be interpreted as systems of structural equations with correlated errors. This enables us to adapt Pearl's do-calculus to them. Finally, we describe an exact algorithm for learning the new models from observational and interventional data via answer set programming.

翻译：我们扩展了安德森-Madigan-Perlman链条图,方法是:(一) 放松半定向环球限制,只禁止定向周期,以及(二) 允许任何对结点之间的两个边缘。我们引入了全球,并为新模型订购了本地和对称的马尔科夫属性。我们用绝对正概率分布来显示这些属性的等值。我们还显示,当随机变量是连续的时,新模型可以被解释为结构方程系统,带有相关错误。这使我们能够根据它们调整珀尔的计算方法。最后,我们描述了一种精确的算法,用于通过应答组合程序从观测和干预数据中学习新模型。