We present a very general approach to learning the structure of causal models based on d-separation constraints, obtained from any given set of overlapping passive observational or experimental data sets. The procedure allows for both directed cycles (feedback loops) and the presence of latent variables. Our approach is based on a logical representation of causal pathways, which permits the integration of quite general background knowledge, and inference is performed using a Boolean satisfiability (SAT) solver. The procedure is complete in that it exhausts the available information on whether any given edge can be determined to be present or absent, and returns "unknown" otherwise. Many existing constraint-based causal discovery algorithms can be seen as special cases, tailored to circumstances in which one or more restricting assumptions apply. Simulations illustrate the effect of these assumptions on discovery and how the present algorithm scales.

本文提出了一种非常通用的方法来学习因果模型的结构，该方法基于从任何给定的重叠的被动观察或实验性数据集获得的d-分离约束。此方法允许直接循环（反馈回路）和潜在变量的存在。我们的方法基于因果路径的逻辑表示，允许将相当通用的背景知识集成，推理是使用布尔满足（SAT）求解器执行的。该过程是完整的，因为它用尽了关于是否可以确定存在或不存在任何给定边缘的可用信息，否则返回“未知”。许多现有的基于约束的因果发现算法可以看作是特殊情况，适用于一个或多个限制性假设的情况。模拟说明了这些假设对发现的影响以及现有算法的扩展能力。

使用潜变量发现循环因果模型：一般的基于 SAT 算法的过程