摘要翻译：
我们考虑离散图形模型混合的无监督估计，其中混合分量对应的类变量是隐藏的，并且观察变量上的每个混合分量可能具有潜在不同的Markov图结构和参数。我们提出了一种新的估计混合分量的方法，我们的输出是一个树-混合模型，它可以很好地逼近底层的图形模型混合。当混合成分的Markov图的并图在任意一对观测变量之间具有稀疏的顶点分离器时，我们的方法是有效的。这包括树混合和有界度图的混合。对于这样的模型，我们证明了我们的方法正确地恢复了混合成分的并图结构和最大似然树近似对应的树结构。对于由$p$-变量图形模型组成的$r$-组件混合物，我们的方法的样本和计算复杂度为$\poly(p，r)$。我们进一步将我们的结果推广到联合图中任意一对观测变量之间有稀疏的局部分隔符的情况，例如局部树状图的混合，并且混合分量处于相关衰减状态。
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英文标题：
《Learning High-Dimensional Mixtures of Graphical Models》
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作者：
A. Anandkumar, D. Hsu, F. Huang and S. M. Kakade
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最新提交年份：
2012
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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：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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英文摘要：
  We consider unsupervised estimation of mixtures of discrete graphical models, where the class variable corresponding to the mixture components is hidden and each mixture component over the observed variables can have a potentially different Markov graph structure and parameters. We propose a novel approach for estimating the mixture components, and our output is a tree-mixture model which serves as a good approximation to the underlying graphical model mixture. Our method is efficient when the union graph, which is the union of the Markov graphs of the mixture components, has sparse vertex separators between any pair of observed variables. This includes tree mixtures and mixtures of bounded degree graphs. For such models, we prove that our method correctly recovers the union graph structure and the tree structures corresponding to maximum-likelihood tree approximations of the mixture components. The sample and computational complexities of our method scale as $\poly(p, r)$, for an $r$-component mixture of $p$-variate graphical models. We further extend our results to the case when the union graph has sparse local separators between any pair of observed variables, such as mixtures of locally tree-like graphs, and the mixture components are in the regime of correlation decay.
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PDF链接：
https://arxiv.org/pdf/1203.0697