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

Abstract: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.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI)

arXiv:2610.28134 [cs.LG]

(or arXiv:2610.28134v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.28134 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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