极大祖先图的马尔可夫性质研究

Markov Properties for Maximal Ancestral Graphs

极大祖先图可编码为含有潜变量的有向无圈图模型的条件独立性关系。不同的极大祖先图可表示相同的条件独立集,称之为马尔可夫等价。基于有向无圈图模型,给出了构造极大祖先图的算法,研究了极大祖先图的马尔可夫性质,并给出了构造极大祖先图马尔可夫等价类的方向准则。

Maximal ancestral graphs can encode conditional independence relations of directed acyclic graphs with latent variables. Different maximal ancestral graphs may be Markov equivalent in the sense that they entail the same conditional independent relations.Based on the model of directed acyclic graphs, an algorithm for constructing maximal ancestral graphs is given, and the Markov properties of maximal ancestral graphs are discussed. Finally, a set of orientation rules is presented that construct the Markov equivalence class representative given a member of the equivalence class.