A method of network filtering has been proposed recently to detect the effects of certain external perturbations on the interacting members in a network. However, with large networks, the goal of detection seems a priori difficult to achieve, especially since the number of observations available often is much smaller than the number of variables describing the effects of the underlying network. Under the assumption that the network possesses a certain sparsity property, we provide a formal characterization of the accuracy with which the external effects can be detected, using a network filtering system that combines Lasso regression in a sparse simultaneous equation model with simple residual analysis. We explore the implications of the technical conditions underlying our characterization, in the context of various network topologies, and we illustrate our method using simulated data.

中文翻译：

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通过网络过滤进行目标检测

最近提出了一种网络过滤方法来检测某些外部扰动对网络中交互成员的影响。然而，对于大型网络，检测目标似乎很难实现，特别是因为可用观察的数量通常远小于描述底层网络影响的变量数量。在网络具有一定稀疏性的假设下，我们使用网络过滤系统将稀疏联立方程模型中的套索回归与简单的残差分析相结合，提供了可以检测外部影响的准确性的正式表征。我们在各种网络拓扑的背景下探索了我们表征背后的技术条件的含义，