Directed acyclic graphs have been used fruitfully to represent causal
strucures (Pearl 1988). However, in the social sciences and elsewhere models
are often used which correspond both causally and statistically to directed
graphs with directed cycles (Spirtes 1995). Pearl (1993) discussed predicting
the effects of intervention in models of this kind, so-called linear
non-recursive structural equation models. This raises the question of whether
it is possible to make inferences about causal structure with cycles, form
sample data. In particular do there exist general, informative, feasible and
reliable precedures for inferring causal structure from conditional
independence relations among variables in a sample generated by an unknown
causal structure? In this paper I present a discovery algorithm that is correct
in the large sample limit, given commonly (but often implicitly) made plausible
assumptions, and which provides information about the existence or
non-existence of causal pathways from one variable to another. The algorithm is
polynomial on sparse graphs.

本文介绍了一个可以通过样本数据推理带循环因果图的因果结构的发现算法，并给出了正确性条件，该算法是稀疏图上的多项式。

有向循环图的发现算法

A Discovery Algorithm for Directed Cyclic Graphs

We generalize Shimizu et al's (2006) ICA-based approach for discovering
linear non-Gaussian acyclic (LiNGAM) Structural Equation Models (SEMs) from
causally sufficient, continuous-valued observational data. By relaxing the
assumption that the generating SEM's graph is acyclic, we solve the more
general problem of linear non-Gaussian (LiNG) SEM discovery. LiNG discovery
algorithms output the distribution equivalence class of SEMs which, in the
large sample limit, represents the population distribution. We apply a LiNG
discovery algorithm to simulated data. Finally, we give sufficient conditions
under which only one of the SEMs in the output class is 'stable'.

本篇论文通过 IC​​A 方法，利用连续观测数据，发现了线性非高斯的因果结构模型 (LiNGAM-SEM)。该 LiNGAM 发现算法所输出的 SEM 分布等价类在大样本情况下是种群分布，并提出了仅有其中一个 SEM 稳定的充分条件。