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摘要翻译：
不同的有向无环图可能是马尔可夫等价的，因为它们在观察变量之间具有相同的条件独立关系。Chickering(1995)给出了DAGs（不含潜在变量）的Markov等价性的一个变换刻划，这对于导出Markov等价DAGs共有的性质是有用的，并且在一定的推广下，证明Markov等价类上的搜索过程的渐近正确性是必要的，即GES算法。对于具有潜在变量的DAG模型，极大祖先图（MAGs）提供了一个简洁的表示，方便了模型搜索。然而，还没有类似于Chickering的Markov等价MAGs的变换表征。本文为有向MAG建立了这样一个表征，我们期望它将有类似于DAG的用途。
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英文标题：
《A Transformational Characterization of Markov Equivalence for Directed
Acyclic Graphs with Latent Variables》
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作者：
Jiji Zhang, Peter L. Spirtes
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最新提交年份：
2012
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分类信息：
一级分类：Computer Science 计算机科学
二级分类：Artificial Intelligence 人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Statistics 统计学
二级分类：Methodology 方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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英文摘要：
Different directed acyclic graphs (DAGs) may be Markov equivalent in the sense that they entail the same conditional independence relations among the observed variables. Chickering (1995) provided a transformational characterization of Markov equivalence for DAGs (with no latent variables), which is useful in deriving properties shared by Markov equivalent DAGs, and, with certain generalization, is needed to prove the asymptotic correctness of a search procedure over Markov equivalence classes, known as the GES algorithm. For DAG models with latent variables, maximal ancestral graphs (MAGs) provide a neat representation that facilitates model search. However, no transformational characterization -- analogous to Chickering's -- of Markov equivalent MAGs is yet available. This paper establishes such a characterization for directed MAGs, which we expect will have similar uses as it does for DAGs.
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PDF链接：
https://arxiv.org/pdf/1207.1419
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