Sparse estimation of huge networks with a block-wise structure
Sparse estimation of huge networks with a block-wise structure
复制标题
具有分块结构的大型网络的稀疏估计
DOI：
10.1111/ectj.12078
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Moscone F
中科院分区：
文献类型：
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作者：
Moscone F
具有大量节点的网络出现在许多应用领域，对传统的高斯图形建模方法提出了挑战。在本文中，我们主要研究了当变量之间的依赖具有块结构时高斯图形模型的估计。我们提出了逆协方差矩阵的惩罚似然估计，也称为图形LASSO，应用于观测的块平均，并推导了它的渐近性质。蒙特卡罗实验，将我们的估计器与传统的图形LASSO的特性进行比较，表明所提出的方法在存在块依赖结构的情况下工作良好，并且对可能的模型错误规范也具有鲁棒性。最后，我们对1980 - 2012年1088个欧洲小地区的经济增长与趋同进行了实证研究。虽然需要块结构上的优先级信息（例如由数据的层次结构给出），但我们的方法可以用于使用非常大的面板数据集进行估计和预测。此外，当存在缺失值和异常值的问题时，或者当分析的重点是样本外预测时，它特别有用。
Networks with a very large number of nodes appear in many application areas and pose challenges for traditional Gaussian graphical modelling approaches. In this paper, we focus on the estimation of a Gaussian graphical model when the dependence between variables has a block‐wise structure. We propose a penalized likelihood estimation of the inverse covariance matrix, also called Graphical LASSO, applied to block averages of observations, and we derive its asymptotic properties. Monte Carlo experiments, comparing the properties of our estimator with those of the conventional Graphical LASSO, show that the proposed approach works well in the presence of block‐wise dependence structure and that it is also robust to possible model misspecification. We conclude the paper with an empirical study on economic growth and convergence of 1,088 European small regions in the years 1980 to 2012. While requiringa prioriinformation on the block structure – e.g. given by the hierarchical structure of data – our approach can be adopted for estimation and prediction using very large panel data sets. Also, it is particularly useful when there is a problem of missing values and outliers or when the focus of the analysis is on out‐of‐sample prediction.