论文标题
树状线性因果模型中的识别
Identification in Tree-shaped Linear Structural Causal Models
论文作者
论文摘要
线性结构方程模型表示直接因果关系，如指示边缘和混杂因素作为双向边缘。一个开放的问题是从节点之间的相关性识别因果参数。我们调查了其定向组件形成树的模型，并表明，除了经典的仪器变量外，还可以使用丢失的双向边缘周期来识别模型。它们可以产生我们明确求解的二次方程的系统，以获得相邻有向边的因果参数的一两个解决方案。我们展示了如何将多个丢失的周期组合在一起以获得独特的解决方案。这导致了一种算法，该算法可以识别基于Gröbner碱基的先前所需方法，这些实例在结构参数的数量中具有双重指数的时间复杂性。
Linear structural equation models represent direct causal effects as directed edges and confounding factors as bidirected edges. An open problem is to identify the causal parameters from correlations between the nodes. We investigate models, whose directed component forms a tree, and show that there, besides classical instrumental variables, missing cycles of bidirected edges can be used to identify the model. They can yield systems of quadratic equations that we explicitly solve to obtain one or two solutions for the causal parameters of adjacent directed edges. We show how multiple missing cycles can be combined to obtain a unique solution. This results in an algorithm that can identify instances that previously required approaches based on Gröbner bases, which have doubly-exponential time complexity in the number of structural parameters.
