摘要翻译：
我们提出了一种表示随机过程网络的图形模型--最小生成模型图。它是基于随着时间的联合分布的简化因子分解。在适当的条件下，我们证明了它与另一种基于Granger因果关系推广的有向信息图模型是唯一的，并且是一致的。我们演示了在一个特定的序列预测环境中，有向信息是如何量化格兰杰因果关系的。我们还开发了有效的方法，从数据估计拓扑结构，避免了估计联合统计量。一种算法假定度的上限，并使用必要的最小维统计量。在上界无效的情况下，得到的图仍然是一个最佳近似。另一种算法在不知道边界但分布满足某一准则的情况下使用近极小维统计量。类似于无向图形模型的结构学习算法使用互信息估计，这些算法使用有向信息估计。我们刻画了两个插入式有向信息估计的样本复杂度，并得到了置信区间。对于点估计不可靠的情况，我们提出了一种利用置信区间来识别对估计误差具有鲁棒性的最佳逼近的算法。最后，通过对Twitter网络的合成数据和实际数据的分析，验证了所提算法的有效性。在后一种情况下，我们仅仅通过分析推特的时间来确定哪些新闻来源影响了网络中的用户。
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英文标题：
《Directed Information Graphs》
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作者：
Christopher J. Quinn, Negar Kiyavash, and Todd P. Coleman
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最新提交年份：
2015
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Information Theory        信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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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：Mathematics        数学
二级分类：Information Theory        信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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英文摘要：
  We propose a graphical model for representing networks of stochastic processes, the minimal generative model graph. It is based on reduced factorizations of the joint distribution over time. We show that under appropriate conditions, it is unique and consistent with another type of graphical model, the directed information graph, which is based on a generalization of Granger causality. We demonstrate how directed information quantifies Granger causality in a particular sequential prediction setting. We also develop efficient methods to estimate the topological structure from data that obviate estimating the joint statistics. One algorithm assumes upper-bounds on the degrees and uses the minimal dimension statistics necessary. In the event that the upper-bounds are not valid, the resulting graph is nonetheless an optimal approximation. Another algorithm uses near-minimal dimension statistics when no bounds are known but the distribution satisfies a certain criterion. Analogous to how structure learning algorithms for undirected graphical models use mutual information estimates, these algorithms use directed information estimates. We characterize the sample-complexity of two plug-in directed information estimators and obtain confidence intervals. For the setting when point estimates are unreliable, we propose an algorithm that uses confidence intervals to identify the best approximation that is robust to estimation error. Lastly, we demonstrate the effectiveness of the proposed algorithms through analysis of both synthetic data and real data from the Twitter network. In the latter case, we identify which news sources influence users in the network by merely analyzing tweet times.
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PDF链接：
https://arxiv.org/pdf/1204.2003