有向无圈图中的矩阵表示与独立性
Matrix representations and independencies in directed acyclic graphs
摘要：
对于一个有向无圈图，有两个已知的标准来决定是否任何特定的条件独立性声明是隐含的所有分布，根据给定的图的因式分解。这两个标准都是基于图中的特殊类型的路径。它们被称为分离准则，因为在图论意义上，只要条件集是分离集，独立性就成立。我们介绍并讨论了一种替代方法，使用二进制矩阵表示的图形中，零表示独立的声明。一个矩阵条件示出给一个新的路径分离的标准，并相当于前两个路径标准。
英文摘要：
For a directed acyclic graph, there are two known criteria to decide whether any specific conditional independence statement is implied for all distributions factorized according to the given graph. Both criteria are based on special types of path in graphs. They are called separation criteria because independence holds whenever the conditioning set is a separating set in a graph theoretical sense. We introduce and discuss an alternative approach using binary matrix representations of graphs in which zeros indicate independence statements. A matrix condition is shown to give a new path criterion for separation and to be equivalent to each of the previous two path criteria.
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