We consider recovering causal structure from multivariate observational data. We assume the data arise from a linear structural equation model (SEM) in which the idiosyncratic errors are allowed to be dependent in order to capture possible latent confounding. Each SEM can be represented by a graph where vertices represent observed variables, directed edges represent direct causal effects, and bidirected edges represent dependence among error terms. Specifically, we assume that the true model corresponds to a bow-free acyclic path diagram; i.e., a graph that has at most one edge between any pair of nodes and is acyclic in the directed part. We show that when the errors are non-Gaussian, the exact causal structure encoded by such a graph, and not merely an equivalence class, can be recovered from observational data. The method we propose for this purpose uses estimates of suitable moments, but, in contrast to previous results, does not require specifying the number of latent variables a priori. We also characterize the output of our procedure when the assumptions are violated and the true graph is acyclic, but not bow-free. We illustrate the effectiveness of our procedure in simulations and an application to an ecology data set.

翻译：我们考虑从多变量观测数据中恢复因果结构。 我们假设数据来自线性结构方程模型( SEM ), 该模型允许根据特异性错误来捕捉可能的潜伏混淆。 每个 SEM 都可以用一个图表来表示, 该图的脊椎代表观察到的变量, 定向边缘代表直接的因果关系, 双向边缘代表错误术语之间的依赖性。 具体地说, 我们假设真实的模型对应的是无弓环绕路径图; 也就是说, 该图最多处于任何节点之间的一个边缘, 并且是方向部分的周期性 。 我们显示, 当错误是非毛利时, 由这种图表编码的精确因果结构, 而不仅仅是等值类, 可以从观测数据中恢复。 我们为此建议的方法使用适当时间的估计数, 但与先前的结果相反, 我们并不要求先订出潜在变量的数量 。 当假设被违反时, 我们的程序输出在真实的图形是周期性的, 而不是无弓形的。 我们用一个模型来说明我们的程序的有效性 。