# Multivariate Counterfactual Systems And Causal Graphical Models

arXiv: https://arxiv.org/abs/2008.06017 · HTML: https://mlsanity.com/paper/2008.06017/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2020.

## Built on by (most cited first, 9 of 9)

- [The Proximal ID Algorithm](https://mlsanity.com/paper/2108.06818/) (2021)
- [On Testability of the Front-Door Model via Verma Constraints](https://mlsanity.com/paper/2203.00161/) (2022)
- [When does the ID algorithm fail?](https://mlsanity.com/paper/2307.03750/) (2023)
- [Sequential Conditional Transport on Probabilistic Graphs for Interpretable Counterfactual Fairness](https://mlsanity.com/paper/2408.03425/) (2024)
- [Entropic Inequality Constraints from e-separation Relations in Directed Acyclic Graphs with Hidden Variables](https://mlsanity.com/paper/2107.07087/) (2021)
- [Efficient Counterfactual Reasoning in ProbLog via Single World Intervention Programs](https://mlsanity.com/paper/2603.20505/) (2026)
- [Path-specific Effects Based on Information Accounts of Causality](https://mlsanity.com/paper/2106.03178/) (2021)
- [On the physics of nested Markov models: a generalized probabilistic theory perspective](https://mlsanity.com/paper/2411.11614/) (2024)
- [A Characterization of the Orthocomplement of the Tangent Space of Semiparametric Markov Models](https://mlsanity.com/paper/2607.23439/) (2026)

## Abstract (arXiv)

Among Judea Pearl's many contributions to Causality and Statistics, the graphical d-separation} criterion, the do-calculus and the mediation formula stand out. In this chapter we show that d-separation} provides direct insight into an earlier causal model originally described in terms of potential outcomes and event trees. In turn, the resulting synthesis leads to a simplification of the do-calculus that clarifies and separates the underlying concepts, and a simple counterfactual formulation of a complete identification algorithm in causal models with hidden variables.