Linear structural causal models (SCMs)-- in which each observed variable is generated by a subset of the other observed variables as well as a subset of the exogenous sources-- are pervasive in causal inference and casual discovery. However, for the task of causal discovery, existing work almost exclusively focus on the submodel where each observed variable is associated with a distinct source with non-zero variance. This results in the restriction that no observed variable can deterministically depend on other observed variables or latent confounders. In this paper, we extend the results on structure learning by focusing on a subclass of linear SCMs which do not have this property, i.e., models in which observed variables can be causally affected by any subset of the sources, and are allowed to be a deterministic function of other observed variables or latent confounders. This allows for a more realistic modeling of influence or information propagation in systems. We focus on the task of causal discovery form observational data generated from a member of this subclass. We derive a set of necessary and sufficient conditions for unique identifiability of the causal structure. To the best of our knowledge, this is the first work that gives identifiability results for causal discovery under both latent confounding and deterministic relationships. Further, we propose an algorithm for recovering the underlying causal structure when the aforementioned conditions are satisfied. We validate our theoretical results both on synthetic and real datasets.
翻译:每个观察到的线性结构性因果模型(SCMs)——每个观察到的变量都是由其他观察到的变量的一个子类以及外源的一个子项产生——都是因果推断和偶然发现中普遍存在的。然而,为了进行因果发现,现有工作几乎完全侧重于子模型,每个观察到的变量都与非零差异的不同来源相关联。这导致一个限制,即任何观察到的变量都无法决定性地依赖其他观察到的变量或潜在混解者。在本文中,我们扩展结构学习的结果,侧重于没有这种属性的线性 SMs子类子类,即观测到的变量可能因果受到任何源子影响的模型,并允许其他观察到的变量或潜在共集体的确定性功能。这导致一个更现实的模型,即没有观察到的变量可以确定取决于其他观察到的变量或非零差异。我们侧重于从这一子类成员产生的因果发现形式的观测数据。我们从一系列必要和充分的条件中找出一个独特的因果结构,即:所观察到的变量可能受到源性影响的模型可能受到任何来源的因果影响,并被允许成为其他观察到的亚性结构结构的确定性结果。这是我们最深层性结论性结论性结论性结论性结论性结论性结论性结果的,在我们的初始性结论性结论性结果之下,这是我们研究的第一次研究结果。