High-dimensional Gaussian graphical model for network-linked data
High-dimensional Gaussian graphical model for network-linked data
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发表时间：
2019-07
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通讯作者：
Tianxi Li;Cheng Qian;E. Levina;Ji Zhu
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作者：
Tianxi Li;Cheng Qian;E. Levina;Ji Zhu
图形模型通常用于表示变量之间的条件依赖关系。有多种方法可用于从高维数据中探索它们，但几乎所有方法都依赖于观测值独立且同分布的假设。与此同时，通过网络连接的观察变得越来越普遍，并且往往违反这些假设。在这里，我们开发了一个高斯图形模型，用于通过具有潜在不同均值向量的网络连接的观测值，这些均值向量在网络上平滑变化。我们提出了一个有效的估计算法，并证明其有效性的模拟和真实的数据，获得有意义的和可解释的结果统计合作网络。我们还证明了我们的方法在网络内聚性假设下正确地估计了逆协方差矩阵和相应的图结构，网络内聚性是指经验观察到的网络邻居共享相似特征的现象。
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that the observations are independent and identically distributed. At the same time, observations connected by a network are becoming increasingly common, and tend to violate these assumptions. Here we develop a Gaussian graphical model for observations connected by a network with potentially different mean vectors, varying smoothly over the network. We propose an efficient estimation algorithm and demonstrate its effectiveness on both simulated and real data, obtaining meaningful and interpretable results on a statistics coauthorship network. We also prove that our method estimates both the inverse covariance matrix and the corresponding graph structure correctly under the assumption of network âcohesionâ, which refers to the empirically observed phenomenon of network neighbors sharing similar traits.