摘要翻译：
贝叶斯网络是给出联合概率分布的自然和紧凑表示的有用工具。在许多应用中，人们需要从数据中学习贝叶斯网络(BN)。在这种情况下，为了保证一次成功的学习，了解所需样本的数量是很重要的。前人对BNs样本复杂度进行了研究，但主要集中在学习的分布与生成数据的原始分布接近的要求上。在这项工作中，我们研究了学习的一个不同方面，即为了学习正确的网络结构所需的样本数。我们给出了在大样本限制下有效的渐近结果和实验结果，证明了对可行样本容量的学习行为。我们表明，与近似正确的分布相比，结构学习是一项更困难的任务，因为它需要大量的样本，而不管学习者可用的计算能力如何。
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英文标题：
《On the Number of Samples Needed to Learn the Correct Structure of a
  Bayesian Network》
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作者：
Or Zuk, Shiri Margel, Eytan Domany
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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：Machine Learning        机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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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：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：
  Bayesian Networks (BNs) are useful tools giving a natural and compact representation of joint probability distributions. In many applications one needs to learn a Bayesian Network (BN) from data. In this context, it is important to understand the number of samples needed in order to guarantee a successful learning. Previous work have studied BNs sample complexity, yet it mainly focused on the requirement that the learned distribution will be close to the original distribution which generated the data. In this work, we study a different aspect of the learning, namely the number of samples needed in order to learn the correct structure of the network. We give both asymptotic results, valid in the large sample limit, and experimental results, demonstrating the learning behavior for feasible sample sizes. We show that structure learning is a more difficult task, compared to approximating the correct distribution, in the sense that it requires a much larger number of samples, regardless of the computational power available for the learner.
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PDF链接：
https://arxiv.org/pdf/1206.6862