Causal discovery aims to identify causal relationships among variables from observational or interventional data, typically represented by a directed acyclic graph (DAG). The causal invariance principle enables the identification of the causal parents of target variables by exploiting the stability of causal effects across different experimental settings. When some parents are unobserved, however, the induced graph over the observed variables may no longer be a DAG, and it may not be unique, complicating causal inference. For relevant configurations of latent parents, we characterize the induced graph and formalize the conditions under which causal invariance is preserved for the identification of the observed parents. Necessary and sufficient conditions for testing such invariance are formally established for a multivariate Gaussian target.

翻译：因果发现旨在从观测或干预数据中识别变量间的因果关系，通常以有向无环图（DAG）表示。因果不变性原理通过利用因果效应在不同实验设置下的稳定性，能够识别目标变量的因果父节点。然而，当某些父节点未被观测到时，观测变量上的导出图可能不再是DAG，且其结构可能不唯一，从而增加了因果推断的复杂性。针对潜父节点的相关配置，我们刻画了导出图的结构，并形式化了在识别观测父节点时保持因果不变性的条件。针对多元高斯目标变量，我们严格建立了检验此类不变性的充要条件。