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.

翻译：我们研究存在潜在混杂时线性高斯结构方程模型的结构学习问题。现有连续方法在误差独立时表现优异，而先解混杂流程依赖于普遍因子结构或非线性。我们提出\textsc{DECOR}——一种基于似然的完全可微估计器，能联合学习有向无环图和相关噪声模型。我们的理论给出了全局参数可识别性的简明充分条件：若混合图满足弓形自由特性且噪声协方差具有一致特征值边界，则从$(\B,\OmegaMat)$到观测协方差的映射是单射，从而有向结构和噪声均可唯一确定。该估计器交替执行平滑无环图更新与凸噪声更新，可包含轻量级弓形互补惩罚或事后协调步骤。在变化混杂密度、图密度、潜在秩和维度（满足$n<p$）的合成基准测试中，\textsc{DECOR}达到或超越强基线方法，在非普遍混杂场景下表现出特别强的鲁棒性，同时在普遍混杂情况下仍保持竞争力。