Learning Loopy Graphical Models with Latent Variables: Efficient Methods and Guarantees
Learning Loopy Graphical Models with Latent Variables: Efficient Methods and Guarantees
复制标题
学习具有潜在变量的循环图模型：有效的方法和保证
DOI：
10.1214/12-aos1070
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
R. Valluvan
中科院分区：
文献类型：
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作者：
Anima Anandkumar;R. Valluvan
研究了含潜变量图模型的结构估计问题。我们刻画了易处理图估计的条件，并开发了具有可证明保证的有效方法。我们考虑模型的基础马尔可夫图是局部树状的，该模型是在相关衰减的制度。对于Ising模型的特殊情况，我们方法的结构一致性所需的样本数n为n=Ω（θ^（−δη（η+1）−2）_（min）log p），其中p为变量数，θ_（min）为最小边势，δ为深度（即，从隐藏节点到最近的观察节点的距离），并且η是取决于伊辛模型中的节点和边缘势的界限的参数。任何算法下的结构一致性的必要条件，推导出我们的方法几乎匹配的样本要求的下限。此外，所提出的方法是实际的实施，并提供了灵活性，以控制输出图中的潜变量的数量和周期长度。
The problem of structure estimation in graphical models with latent variables is considered. We characterize conditions for tractable graph estimation and develop efficient methods with provable guarantees. We consider models where the underlying Markov graph is locally tree-like, and the model is in the regime of correlation decay. For the special case of the Ising model, the number of samples n required for structural consistency of our method scales as n=Ω(θ^(−δη(η+1)−2)_(min)log p), where p is the number of variables, θ_(min) is the minimum edge potential, δ is the depth (i.e., distance from a hidden node to the nearest observed nodes), and η is a parameter which depends on the bounds on node and edge potentials in the Ising model. Necessary conditions for structural consistency under any algorithm are derived and our method nearly matches the lower bound on sample requirements. Further, the proposed method is practical to implement and provides flexibility to control the number of latent variables and the cycle lengths in the output graph.