DAG DECORation: Continuous Optimization for Structure Learning under Hidden Confounding

• URL: http://arxiv.org/abs/2510.02117v1
• Date: Thu, 02 Oct 2025 15:23:30 GMT
• Title: DAG DECORation: Continuous Optimization for Structure Learning under Hidden Confounding
• Authors: Samhita Pal, James O'quinn, Kaveh Aryan, Heather Pua, James P. Long, Amir Asiaee,
• Abstract summary: We study structure learning for linear Gaussian SEMs in the presence of latent confounding.<n>We propose textscDECOR, a single likelihood-based estimator that jointly learns a DAG and a correlated noise model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We study structure learning for linear Gaussian SEMs in the presence of latent confounding. Existing continuous methods excel when errors are independent, while deconfounding-first pipelines rely on pervasive factor structure or nonlinearity. We propose \textsc{DECOR}, a single likelihood-based and fully differentiable estimator that jointly learns a DAG and a correlated noise model. Our theory gives simple sufficient conditions for global parameter identifiability: if the mixed graph is bow free and the noise covariance has a uniform eigenvalue margin, then the map from $(\B,\OmegaMat)$ to the observational covariance is injective, so both the directed structure and the noise are uniquely determined. The estimator alternates a smooth-acyclic graph update with a convex noise update and can include a light bow complementarity penalty or a post hoc reconciliation step. On synthetic benchmarks that vary confounding density, graph density, latent rank, and dimension with $n<p$, \textsc{DECOR} matches or outperforms strong baselines and is especially robust when confounding is non-pervasive, while remaining competitive under pervasiveness.

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