在有限数据下准确估计高斯线性因果模型的因果效应
Estimating Causal Effects in Gaussian Linear SCMs with Finite Data
- 提出简化版高斯线性因果模型（CGL-SCM），解决参数不可估问题
- 基于EM算法从有限观测数据中学习模型并准确恢复因果分布
- 适合需要可靠因果推断的科研与工业场景
从观测数据中估计因果效应仍是因果推断中的核心挑战，尤其在存在隐变量混杂时。本文聚焦于高斯线性结构因果模型（GL-SCMs），因其解析可处理性被广泛使用。然而，由于参数过多，在有限数据下常难以进行参数估计。为此，我们引入一类新的中心化高斯线性因果模型（CGL-SCMs），其外生变量服从标准化分布。我们证明CGL-SCMs在因果效应可识别性上与原模型等价，并提出一种基于期望最大化（EM）的新算法，可从有限观测样本中学习参数并估计可识别的因果效应。理论分析通过合成数据和基准因果图实验验证，结果表明所学模型能准确恢复因果分布。
原文摘要 · Abstract (English)
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.
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