We consider the problem of recovering the causal structure underlying observations from different experimental conditions when the targets of the interventions in each experiment are unknown. We assume a linear structural causal model with additive Gaussian noise and consider interventions that perturb their targets while maintaining the causal relationships in the system. Different models may entail the same distributions, offering competing causal explanations for the given observations. We fully characterize this equivalence class and offer identifiability results, which we use to derive a greedy algorithm called GnIES to recover the equivalence class of the data-generating model without knowledge of the intervention targets. In addition, we develop a novel procedure to generate semi-synthetic data sets with known causal ground truth but distributions closely resembling those of a real data set of choice. We leverage this procedure and evaluate the performance of GnIES on synthetic, real, and semi-synthetic data sets. Despite the strong Gaussian distributional assumption, GnIES is robust to an array of model violations and competitive in recovering the causal structure in small- to large-sample settings. We provide, in the Python packages "gnies" and "sempler", implementations of GnIES and our semi-synthetic data generation procedure.
翻译:当每次实验的干预目标不明时,我们考虑从不同的实验条件下恢复作为观察基础的因果结构的问题;我们假设一个具有添加性高斯噪音的线性结构性因果模型,并考虑在维持系统内因果关系的同时干扰目标的干预;不同模型可能包含同样的分布,为特定观测提供相互竞争的因果解释;我们充分描述这一等值类别并提供可识别性结果,我们用它来得出一种贪婪的算法,称为GNIES,以便在不知晓干预目标的情况下恢复数据生成模型的等值等级;此外,我们开发了一种新型程序,以生成半合成数据集,其中含有已知因果地面真相,但分布与真实数据组合的相似;我们利用这一程序并评估GNIES在合成、真实和半合成数据集上的性能;尽管高斯分布假设十分强烈,但GNIES在小至大型环境中恢复因果结构时,对一系列模型违规性和竞争力十分强大。我们在Python 包“gnes”和“semental IISs” 和“semental produments and Gynal productions”。