摘要翻译：
假设多个专家（或学习算法）在一个域上为我们提供了可供选择的贝叶斯网络(BN)结构，并且我们有兴趣将它们组合成一个单一的一致BN结构。具体地说，我们感兴趣的是，一致的BN结构只代表所有给定的BN结构都同意的独立性，并且它有尽可能少的相关参数。本文证明了可能存在几种非等价的一致BN结构，并且证明了寻找其中一种结构是NP难的。因此，我们决定采用启发式方法来寻找一个近似的一致BN结构。本文考虑了Citep{MatzkevichandAbramson1992,MatzkevichandAbramson1993a,MatzkevichandAbramson1993b}中提出的启发式。这种启发式建立在两种算法上，称为方法A和方法B，用于有效地导出BN结构相对于给定节点排序的最小有向独立映射。方法A和B被认为是正确的，尽管没有提供证明（A证明只是草图）。在本文中，我们证明了方法A和方法B是不正确的，并提出了对它们的修正。
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英文标题：
《Finding Consensus Bayesian Network Structures》
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作者：
Jose M. Pe\~na
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最新提交年份：
2011
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分类信息：

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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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：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  Suppose that multiple experts (or learning algorithms) provide us with alternative Bayesian network (BN) structures over a domain, and that we are interested in combining them into a single consensus BN structure. Specifically, we are interested in that the consensus BN structure only represents independences all the given BN structures agree upon and that it has as few parameters associated as possible. In this paper, we prove that there may exist several non-equivalent consensus BN structures and that finding one of them is NP-hard. Thus, we decide to resort to heuristics to find an approximated consensus BN structure. In this paper, we consider the heuristic proposed in \citep{MatzkevichandAbramson1992,MatzkevichandAbramson1993a,MatzkevichandAbramson1993b}. This heuristic builds upon two algorithms, called Methods A and B, for efficiently deriving the minimal directed independence map of a BN structure relative to a given node ordering. Methods A and B are claimed to be correct although no proof is provided (a proof is just sketched). In this paper, we show that Methods A and B are not correct and propose a correction of them.
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PDF链接：
https://arxiv.org/pdf/1101.1715