论文标题
线性结构方程模型中的多行程分离
Multi-trek separation in Linear Structural Equation Models
论文作者
论文摘要
在观察数据中的因果发现理论的基础上，我们研究了具有非高斯误差项的线性结构方程模型中多个（集合）随机变量之间的相互作用。我们在因果图中的高阶累积物和组合结构中给出了对应关系。先前已经显示，协方差矩阵的低等级对应于图中的跋涉分离。将此标准概括为多组顶点，我们表征了高阶累积张量的子镜的决定因素消失时。当存在隐藏变量时，此标准也适用。例如，它使我们能够确定观察到的变量的k的隐藏共同原因。
Building on the theory of causal discovery from observational data, we study interactions between multiple (sets of) random variables in a linear structural equation model with non-Gaussian error terms. We give a correspondence between structure in the higher order cumulants and combinatorial structure in the causal graph. It has previously been shown that low rank of the covariance matrix corresponds to trek separation in the graph. Generalizing this criterion to multiple sets of vertices, we characterize when determinants of subtensors of the higher order cumulant tensors vanish. This criterion applies when hidden variables are present as well. For instance, it allows us to identify the presence of a hidden common cause of k of the observed variables.
