In this article, we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model with given observational data. We build on an algorithm proposed by Wang and Drton, and we show that one can augment the hidden variable structure of the recovered model by learning multidirected edges rather than only directed and bidirected ones. Multidirected edges appear when more than two of the observed variables have a hidden common cause. We detect the presence of such hidden causes by looking at higher order cumulants and exploiting the multi-trek rule. Our method recovers the correct structure when the underlying graph is a bow-free acyclic mixed graph with potential multidirected edges.

中文翻译：

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学习具有多向边的线性非高斯图模型

在本文中，我们提出了一种新方法来学习具有给定观测数据的线性非高斯结构方程模型的底层非循环混合图。我们建立在 Wang 和 Drton 提出的算法的基础上，我们表明可以通过学习多向边而不是仅仅定向和双向边来增强恢复模型的隐藏变量结构。当两个以上的观察变量具有隐藏的共同原因时，就会出现多向边。我们通过查看高阶累积量并利用多重跋涉规则来检测这种隐藏原因的存在。当底层图是具有潜在多向边的无弓无环混合图时，我们的方法恢复了正确的结构。