Causal Discovery for Linear Models with Latent Confounding via Multi-domain Identifiable Representation Learning

Danru Xu, Aapo Hyvärinen, Sara Magliacane

Causal discovery with latent confounding is particularly challenging, but a common setting in real-world data. In this work, we focus on linear causal models with latent confounding, represented by acyclic directed mixed graphs (ADMGs). Existing methods that fully identify ADMGs typically assume non-Gaussianity or graphical constraints, such as bow-freeness. In contrast, we propose Linear ADMG Learning (LinADMG), a framework for learning ADMGs for linear causal models through identifiable representation learning. Rather than relying on non-Gaussianity or bow-freeness, LinADMG leverages multi-domain settings to identify the noise variables. We show that the identifiability of the noise variables is sufficient for recovering all direct causal relations, and that, under an additional latent-confounding no-cancellation condition, LinADMG can identify the whole ADMG. We implement LinADMG with four identifiable representation learning approaches from the literature and validate the methods on simulated and semisynthetic datasets.