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.

从多元观测数据中恢复因果关系结构，方法基于线性结构方程模型，可有效处理潜在混淆，并可通过无弓有向无环路径图恢复精确的因果结构。