{"ID":2861541,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.02117","arxiv_id":"2510.02117","title":"DAG DECORation: Continuous Optimization for Structure Learning under Hidden Confounding","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 $n\u003cp$, \\textsc{DECOR} matches or outperforms strong baselines and is especially robust when confounding is non-pervasive, while remaining competitive under pervasiveness.","short_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...","url_abs":"https://arxiv.org/abs/2510.02117","url_pdf":"https://arxiv.org/pdf/2510.02117v1","authors":"[\"Samhita Pal\",\"James O'quinn\",\"Kaveh Aryan\",\"Heather Pua\",\"James P. Long\",\"Amir Asiaee\"]","published":"2025-10-02T15:23:30Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"stat.ME\"]","methods":"[]","has_code":false}