Joint estimation of multiple graphical models
Joint estimation of multiple graphical models
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DOI：
10.1093/biomet/asq060
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发表时间：
2011-03-01
期刊：
影响因子：
2.7
通讯作者：
Zhu, Ji
中科院分区：
文献类型：
--
作者：
Guo, Jian;Levina, Elizaveta;Zhu, Ji
高斯图形模型探索随机变量之间的依赖关系，通过估计相应的逆协方差矩阵。在本文中，我们为这类模型开发了一个估计量，它适用于来自几个具有相同变量和某些依赖结构的图形模型的数据。在这种情况下，估计单个图形模型将掩盖潜在的异质性，而估计每个类别的单独模型并没有利用公共结构。我们提出了一种联合估计数据中不同类别对应的图形模型的方法，旨在保留共同结构，同时允许类别之间的差异。这是通过分层惩罚来实现的，该惩罚的目标是消除跨类别的逆协方差矩阵中的公共零。我们建立了在高维情况下所提出的估计量的渐近一致性和稀疏性，并说明了它在一些模拟网络上的性能。一个应用程序来学习从计算机科学部门收集的网页术语之间的语义连接。
Gaussian graphical models explore dependence relationships between random variables, through the estimation of the corresponding inverse covariance matrices. In this paper we develop an estimator for such models appropriate for data from several graphical models that share the same variables and some of the dependence structure. In this setting, estimating a single graphical model would mask the underlying heterogeneity, while estimating separate models for each category does not take advantage of the common structure. We propose a method that jointly estimates the graphical models corresponding to the different categories present in the data, aiming to preserve the common structure, while allowing for differences between the categories. This is achieved through a hierarchical penalty that targets the removal of common zeros in the inverse covariance matrices across categories. We establish the asymptotic consistency and sparsity of the proposed estimator in the high-dimensional case, and illustrate its performance on a number of simulated networks. An application to learning semantic connections between terms from webpages collected from computer science departments is included.