摘要翻译：
DAG是概率分布独立映射的局部马尔可夫条件是众所周知的。对于具有潜在变量的DAG，在图中表示为双向边，局部马尔可夫性质可以调用指数数的条件独立性。本文表明，当概率分布满足合成公理时，所需的条件独立关系数可以减少。在某些类型的图中，只需要线性数目的条件独立性。该结果可用于检验具有相关误差的线性结构方程模型。
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英文标题：
《Local Markov Property for Models Satisfying Composition Axiom》
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作者：
Changsung Kang, Jin Tian
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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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英文摘要：
  The local Markov condition for a DAG to be an independence map of a probability distribution is well known. For DAGs with latent variables, represented as bi-directed edges in the graph, the local Markov property may invoke exponential number of conditional independencies. This paper shows that the number of conditional independence relations required may be reduced if the probability distributions satisfy the composition axiom. In certain types of graphs, only linear number of conditional independencies are required. The result has applications in testing linear structural equation models with correlated errors.
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PDF链接：
https://arxiv.org/pdf/1207.1378