Estimating Causal Effects in Gaussian Linear SCMs with Finite Data
Aurghya Maiti, Prateek Jain
TL;DR
This work addresses estimating causal effects in Gaussian Linear SCMs when data are finite and latent confounding may be present. It introduces Centralized Gaussian Linear SCMs (CGL-SCMs), a standardized subclass with exogenous variables $U \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$, enabling tractable parameter learning while retaining the same identifiability power as GL-SCMs for observational data. A scalable EM-based estimator is developed in a vectorized form, using masks to enforce graphical constraints, and a second procedure recovers the underlying graph edge weights. Experiments on Frontdoor and Napkin graphs show that the learned CGL-SCMs accurately recover interventional distributions from finite samples, illustrating practical applicability for causal effect estimation under latent confounding.
Abstract
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.