论文标题
ADMG模型的M连接IMSET和分解
The m-connecting imset and factorization for ADMG models
论文作者
论文摘要
定向的无环图（DAG）模型已在统计和机器学习中广泛研究和应用 - 实际上，它们的简单性促进了有效的学习和推理程序。不幸的是，这些模型在边缘化下并未关闭，使它们能够处理具有潜在混杂的系统。无环的有向混合图（ADMG）模型表征了DAG模型的边缘，使其更适合处理此类系统。但是，由于ADMG模型的复杂性和用于分析的统计工具的短缺，因此没有看到广泛使用。在本文中，我们介绍了M连接IMSET，该IMSET为ADMG引起的独立模型提供了另一种表示。此外，我们定义了以单个方程为特征的ADMG模型的M连接分数标准，并证明了其与全球Markov属性的等效性。 M-conting Imset和分解标准提供了两个新的统计工具，用于使用ADMG模型进行学习和推断。我们通过使用封闭形式解决方案制定和评估一致的评分标准来证明这些工具的有用性。
Directed acyclic graph (DAG) models have become widely studied and applied in statistics and machine learning -- indeed, their simplicity facilitates efficient procedures for learning and inference. Unfortunately, these models are not closed under marginalization, making them poorly equipped to handle systems with latent confounding. Acyclic directed mixed graph (ADMG) models characterize margins of DAG models, making them far better suited to handle such systems. However, ADMG models have not seen wide-spread use due to their complexity and a shortage of statistical tools for their analysis. In this paper, we introduce the m-connecting imset which provides an alternative representation for the independence models induced by ADMGs. Furthermore, we define the m-connecting factorization criterion for ADMG models, characterized by a single equation, and prove its equivalence to the global Markov property. The m-connecting imset and factorization criterion provide two new statistical tools for learning and inference with ADMG models. We demonstrate the usefulness of these tools by formulating and evaluating a consistent scoring criterion with a closed form solution.
