Simplifying Probabilistic Expressions in Causal Inference
This work addresses a practical issue for researchers and practitioners in causal inference by providing a tool to simplify expressions, though it is incremental as it builds on existing do-calculus and algorithmic frameworks.
The paper tackles the problem of complex non-parametric expressions for identifiable causal effects in causal inference, which can lead to biased or inefficient estimates, by presenting an automatic simplification algorithm that eliminates unnecessary variables using graphical model structure, resulting in a method applicable to all causal effect formulas and implemented in the R package causaleffect.
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.