Approaches based on Functional Causal Models (FCMs) have been proposed to determine causal direction between two variables, by properly restricting model classes; however, their performance is sensitive to the model assumptions, which makes it difficult for practitioners to use. In this paper, we provide a novel dynamical-system view of FCMs and propose a new framework for identifying causal direction in the bivariate case. We first show the connection between FCMs and optimal transport, and then study optimal transport under the constraints of FCMs. Furthermore, by exploiting the dynamical interpretation of optimal transport under the FCM constraints, we determine the corresponding underlying dynamical process of the static cause-effect pair data under the least action principle. It provides a new dimension for describing static causal discovery tasks, while enjoying more freedom for modeling the quantitative causal influences. In particular, we show that Additive Noise Models (ANMs) correspond to volume-preserving pressureless flows. Consequently, based on their velocity field divergence, we introduce a criterion to determine causal direction. With this criterion, we propose a novel optimal transport-based algorithm for ANMs which is robust to the choice of models and extend it to post-noninear models. Our method demonstrated state-of-the-art results on both synthetic and causal discovery benchmark datasets.
翻译:根据功能性因果关系模型(FCMS)提出方法,通过适当限制模型类别,确定两个变量之间的因果关系方向;然而,其性能对模型假设十分敏感,使从业人员难以使用。在本文件中,我们为FCMS提供了一个全新的动态系统观点,并提出了一个新的框架,用于确定双轨制案例的因果关系方向。我们首先展示了FCM和最佳运输之间的联系,然后研究FCM限制下的最佳运输。此外,通过利用对FCM限制下最佳运输的动态解释,我们根据最小行动原则,确定静态因果配对数据的相应动态过程。它为描述静态因果发现任务提供了一个新的层面,同时享有更自由地模拟数量性因果影响。特别是,我们表明Additive噪音模型(ANMS)与量保留无压力的流动相对应。因此,我们根据速度场差异,引入了确定因果方向的标准。我们根据这一标准,为ANMs提出了一个新的基于动态因果对最小的相对立数据动态动态动态算法,这既能强有力地选择了模型,又扩展了我们的因果性模型。