论文标题
迈向最大祖先图的标准IMSET
Towards standard imsets for maximal ancestral graphs
论文作者
论文摘要
Studený（2005）的IMSET是代表条件独立模型的代数方法。当应用于此类模型时，它们具有许多有吸引力的属性，并且特别适合使用定向的无环图（DAG）模型。特别是，DAG的“标准” IMSET与其引起的独立性一对一，因此是其Markov等价类别的标签。我们首先使用HU和Evans（2020）的参数化集合表示，向最大祖先图（MAG）模型的标准IMSET提出了一个提议的扩展。在这些情况下，IMSET通过测量定义模型的独立性列表来提供评分标准。这为通常的BIC分数提供了替代方案，它也是一致的，并且更容易计算。我们还表明，在代表MAG的独立模型中，我们给出的IMSET是最小的。不幸的是，对于某些图表，表示形式并不代表模型中的所有独立性，并且在某些情况下根本不代表任何独立性。对于这些一般的杂志，我们通过一种名为_power dags_的新型图形工具来完善减少有序的本地马尔可夫属性Richardson（2003），这导致IMSET诱导正确的模型，并且在温和的条件下可以在多项式时间内构建。
The imsets of Studený (2005) are an algebraic method for representing conditional independence models. They have many attractive properties when applied to such models, and they are particularly nice for working with directed acyclic graph (DAG) models. In particular, the 'standard' imset for a DAG is in one-to-one correspondence with the independences it induces, and hence is a label for its Markov equivalence class. We first present a proposed extension to standard imsets for maximal ancestral graph (MAG) models, using the parameterizing set representation of Hu and Evans (2020). In these cases the imset provides a scoring criteria by measuring the discrepancy for a list of independences that define the model; this gives an alternative to the usual BIC score that is also consistent, and much easier to compute. We also show that, of independence models that do represent the MAG, the imset we give is minimal. Unfortunately, for some graphs the representation does not represent all the independences in the model, and in certain cases does not represent any at all. For these general MAGs, we refine the reduced ordered local Markov property Richardson (2003) by a novel graphical tool called _power DAGs_, and this results in an imset that induces the correct model and which, under a mild condition, can be constructed in polynomial time.
