论文标题
线性结构方程模型中的回归可识别性和边缘干预措施
Regression Identifiability and Edge Interventions in Linear Structural Equation Models
论文作者
论文摘要
在本文中，我们介绍了线性结构方程模型的新可识别性标准，我们称之为回归性可识别性。我们提供了必要且足够的图形条件，以使有向边的回归可识别。假设$σ^*$对应于图形模型$ g^*$的协方差矩阵，该矩阵通过将边缘干预对$ g $进行，并具有相应的协方差矩阵$σ$。我们首先获得$σ^*$的必要条件，可以在给定$σ$的情况下。使用回归可识别性，我们获得了$σ^*$的必要图形条件，以给定$σ$。如果有这样的干预，我们还确定了单个数据点会发生什么。最后，我们提供了一些可以使用方法的统计问题，例如查找约束和模拟观察数据的介入数据。
In this paper, we introduce a new identifiability criteria for linear structural equation models, which we call regression identifiability. We provide necessary and sufficient graphical conditions for a directed edge to be regression identifiable. Suppose $Σ^*$ corresponds to the covariance matrix of the graphical model $G^*$ obtained by performing an edge intervention to $G$ with corresponding covariance matrix $Σ$. We first obtain necessary and sufficient conditions for $Σ^*$ to be identifiable given $Σ$. Using regression identifiability, we obtain necessary graphical conditions for $Σ^*$ to be identifiable given $Σ$. We also identify what would happen to an individual data point if there were such an intervention. Finally, we provide some statistical problems where our methods could be used, such as finding constraints and simulating interventional data from observational data.
