Bayesian Model Averaging for Causality Estimation and its Approximation based on Gaussian Scale Mixture Distributions
This work addresses a computational bottleneck for researchers in causal inference, though it is incremental as it builds on existing Bayesian model averaging methods.
The paper tackles the computational challenge of Bayesian model averaging for causal effect estimation in linear Structural Causal Models by proposing an approximation using Gaussian scale mixture distributions, which reduces computational hardness as the number of models increases.
In the estimation of the causal effect under linear Structural Causal Models (SCMs), it is common practice to first identify the causal structure, estimate the probability distributions, and then calculate the causal effect. However, if the goal is to estimate the causal effect, it is not necessary to fix a single causal structure or probability distributions. In this paper, we first show from a Bayesian perspective that it is Bayes optimal to weight (average) the causal effects estimated under each model rather than estimating the causal effect under a fixed single model. This idea is also known as Bayesian model averaging. Although the Bayesian model averaging is optimal, as the number of candidate models increases, the weighting calculations become computationally hard. We develop an approximation to the Bayes optimal estimator by using Gaussian scale mixture distributions.