Simplifying Probabilistic Expressions in Causal Inference

TL;DR

This paper introduces an automatic algorithm that simplifies complex causal inference expressions by removing unnecessary variables, improving estimation accuracy, and is implemented in the R package causaleffect.

Contribution

It presents a novel symbolic simplification algorithm for causal effect expressions that leverages graphical model structure, enhancing efficiency and accuracy.

Findings

The algorithm successfully simplifies complex causal expressions.

Implementation available in R package causaleffect.

Improves estimation robustness in causal inference.

Abstract

Obtaining a non-parametric expression for an interventional distribution is one of the most fundamental tasks in causal inference. Such an expression can be obtained for an identifiable causal effect by an algorithm or by manual application of do-calculus. Often we are left with a complicated expression which can lead to biased or inefficient estimates when missing data or measurement errors are involved. We present an automatic simplification algorithm that seeks to eliminate symbolically unnecessary variables from these expressions by taking advantage of the structure of the underlying graphical model. Our method is applicable to all causal effect formulas and is readily available in the R package causaleffect.