🤖 AI Summary
This work addresses the challenge posed by latent variables, which can induce non-directed acyclic and non-unique causal graphs among observed variables, thereby undermining conventional causal invariance methods. The paper characterizes the structure of such latent-induced observational graphs and, for the first time, establishes rigorous necessary and sufficient conditions for causal invariance in settings involving latent confounders, explicitly delineating its applicability even when the observed graph is not a DAG. Under a multivariate Gaussian assumption, the authors develop a verifiable theoretical framework that integrates causal graphical models with hypothesis testing. When the derived conditions hold, this framework accurately identifies observable causal parents, substantially enhancing the reliability of causal discovery in the presence of latent interference.
📝 Abstract
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.