摘要翻译：
在这篇文章中，我们提出了一个算法来计算一个图形模型的边缘上的边界。对于几个小的节点簇，边缘值的上下界独立于网络的其余部分计算。周围节点上允许的概率分布的范围是使用先前计算的边界来限制的。正如我们将要说明的，这可以看作是线性规划问题中的一组约束，目标函数是中心节点的边际概率。通过这种方式，关于邻近星系团的磁振子的知识被传递给其他星系团，从而收紧了它们边缘的界限。我们证明了对于实际应用中使用的无向图和有向图，可以得到尖锐的界，但对它们的精确计算是不可行的。
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英文标题：
《Bound Propagation》
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作者：
B. Kappen, M. Leisink
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最新提交年份：
2011
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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：
  In this article we present an algorithm to compute bounds on the marginals of a graphical model. For several small clusters of nodes upper and lower bounds on the marginal values are computed independently of the rest of the network. The range of allowed probability distributions over the surrounding nodes is restricted using earlier computed bounds. As we will show, this can be considered as a set of constraints in a linear programming problem of which the objective function is the marginal probability of the center nodes. In this way knowledge about the maginals of neighbouring clusters is passed to other clusters thereby tightening the bounds on their marginals. We show that sharp bounds can be obtained for undirected and directed graphs that are used for practical applications, but for which exact computations are infeasible.
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PDF链接：
https://arxiv.org/pdf/1106.4865