Estimating causal effects from observational data remains a fundamental challenge in causal inference, especially in the presence of latent confounders. This paper focuses on estimating causal effects in Gaussian Linear Structural Causal Models (GL-SCMs), which are widely used due to their analytical tractability. However, parameter estimation in GL-SCMs is often infeasible with finite data, primarily due to overparameterization. To address this, we introduce the class of Centralized Gaussian Linear SCMs (CGL-SCMs), a simplified yet expressive subclass where exogenous variables follow standardized distributions. We show that CGL-SCMs are equally expressive in terms of causal effect identifiability from observational distributions and present a novel EM-based estimation algorithm that can learn CGL-SCM parameters and estimate identifiable causal effects from finite observational samples. Our theoretical analysis is validated through experiments on synthetic data and benchmark causal graphs, demonstrating that the learned models accurately recover causal distributions.

翻译：从观测数据中估计因果效应仍然是因果推断领域的核心挑战，尤其在存在潜在混杂因素的情况下。本文聚焦于高斯线性结构因果模型中的因果效应估计问题，此类模型因其解析上的易处理性而被广泛应用。然而，由于过度参数化问题，在有限数据条件下通常难以对GL-SCMs进行参数估计。为解决此问题，我们引入了集中化高斯线性结构因果模型这一类别，这是一个简化但仍具表达力的子类，其外生变量服从标准化分布。我们证明，在从观测分布识别因果效应的能力方面，CGL-SCMs具有同等的表达力，并提出了一种新颖的基于期望最大化的估计算法，该算法能够从有限的观测样本中学习CGL-SCM参数并估计可识别的因果效应。我们通过合成数据和基准因果图上的实验验证了理论分析，结果表明学习到的模型能够准确恢复因果分布。