Bayesian Model Averaging for Causality Estimation and its Approximation based on Gaussian Scale Mixture Distributions

by   Shunsuke Horii, et al.

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.



page 1

page 2

page 3

page 4


A Note on the Estimation Method of Intervention Effects based on Statistical Decision Theory

In this paper, we deal with the problem of estimating the intervention e...

An integral equation for the identification of causal effects in nonlinear models

When the causal relationship between X and Y is specified by a structura...

Algorithmic recourse under imperfect causal knowledge: a probabilistic approach

Recent work has discussed the limitations of counterfactual explanations...

Averaging causal estimators in high dimensions

There has been increasing interest in recent years in the development of...

"Conditional Inter-Causally Independent" Node Distributions, a Property of "Noisy-Or" Models

This paper examines the interdependence generated between two parent nod...

Hierarchical Bayesian Bootstrap for Heterogeneous Treatment Effect Estimation

A major focus of causal inference is the estimation of heterogeneous ave...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.