# Simplifying Probabilistic Expressions in Causal Inference

arXiv: https://arxiv.org/abs/1806.07082 · HTML: https://mlsanity.com/paper/1806.07082/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jun 2018.

## Built on by (most cited first, 6 of 6)

- [Clustering and Structural Robustness in Causal Diagrams](https://mlsanity.com/paper/2111.04513/) (2021)
- [Identifying Causal Effects Under Functional Dependencies](https://mlsanity.com/paper/2403.04919/) (2024)
- [Unveiling the Structure of Do-Calculus Reasoning via Derivation Graphs](https://mlsanity.com/paper/2606.03719/) (2026)
- [Identifiability of Causal-based Fairness Notions: A State of the Art](https://mlsanity.com/paper/2203.05900/) (2022)
- [Causal identification with Y0](https://mlsanity.com/paper/2508.03167/) (2025)
- [Reasoning Models Are Accurate but Unsound on Identification](https://mlsanity.com/paper/2610.03519/) (2026)

## Abstract (arXiv)

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.