Causal Discovery with Mixed Latent Confounding via Precision Decomposition

We study causal discovery from observational data in linear Gaussian systems affected by mixed latent confounding, where some unobserved factors act broadly across many variables while others influence only small subsets. This setting is common in practice and poses a challenge for existing methods: differentiable and score-based DAG learners can misinterpret global latent effects as causal edges, while latent-variable graphical models recover only undirected structure. We propose textscDCL-DECOR, a modular, precision-led pipeline that separates these roles. The method first isolates pervasive latent effects by decomposing the observed precision matrix into a structured component and a low-rank component. The structured component corresponds to the conditional distribution after accounting for pervasive confounders and retains only local dependence induced by the causal graph and localized confounding. A correlated-noise DAG learner is then applied to this deconfounded representation to recover directed edges while modeling remaining structured error correlations, followed by a simple reconciliation step to enforce bow-freeness. We provide identifiability results that characterize the recoverable causal target under mixed confounding and show how the overall problem reduces to well-studied subproblems with modular guarantees. Synthetic experiments that vary the strength and dimensionality of pervasive confounding demonstrate consistent improvements in directed edge recovery over applying correlated-noise DAG learning directly to the confounded data.