# Comparing Causal Frameworks: Potential Outcomes, Structural Models, Graphs, and Abstractions

arXiv: https://arxiv.org/abs/2306.14351 · HTML: https://mlsanity.com/paper/2306.14351/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 47 references that are in the map.
- First posted on arXiv 25 Jun 2023.

## Builds on (most cited first, 15 of 15)

- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Confounding-Robust Policy Improvement](https://mlsanity.com/paper/1805.08593/) (2018)
- [Causal Networks: Semantics and Expressiveness](https://mlsanity.com/paper/1304.2379/) (2013)
- [Off-Policy Evaluation in Partially Observable Environments](https://mlsanity.com/paper/1909.03739/) (2019)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [Off-policy Policy Evaluation For Sequential Decisions Under Unobserved Confounding](https://mlsanity.com/paper/2003.05623/) (2020)
- [Causal Imitation Learning with Unobserved Confounders](https://mlsanity.com/paper/2208.06267/) (2022)
- [Nested Markov Properties for Acyclic Directed Mixed Graphs](https://mlsanity.com/paper/1701.06686/) (2017)
- [Margins of discrete Bayesian networks](https://mlsanity.com/paper/1501.02103/) (2015)
- [A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects](https://mlsanity.com/paper/1903.03662/) (2019)
- [Probabilistic Reasoning across the Causal Hierarchy](https://mlsanity.com/paper/2001.02889/) (2020)
- [Causal Inference with a Graphical Hierarchy of Interventions](https://mlsanity.com/paper/1411.2127/) (2014)
- [A Topological Perspective on Causal Inference](https://mlsanity.com/paper/2107.08558/) (2021)
- [Is Causal Reasoning Harder than Probabilistic Reasoning?](https://mlsanity.com/paper/2111.13936/) (2021)
- [Causal Modeling With Infinitely Many Variables](https://mlsanity.com/paper/2112.09171/) (2021)

## Built on by (most cited first, 11 of 11)

- [Causal Estimation of Memorisation Profiles](https://mlsanity.com/paper/2406.04327/) (2024)
- [Efficient Computation of Counterfactual Bounds](https://mlsanity.com/paper/2307.08304/) (2023)
- [What is causal about causal models and representations?](https://mlsanity.com/paper/2501.19335/) (2025)
- [On Probabilistic and Causal Reasoning with Summation Operators](https://mlsanity.com/paper/2405.03069/) (2024)
- [Modeling Discrimination with Causal Abstraction](https://mlsanity.com/paper/2501.08429/) (2025)
- [Probabilistic Modelling is Sufficient for Causal Inference](https://mlsanity.com/paper/2512.23408/) (2025)
- [Causal Feature Learning in the Social Sciences](https://mlsanity.com/paper/2503.12784/) (2025)
- [What is a good matching of probability measures? A counterfactual lens on transport maps](https://mlsanity.com/paper/2509.16027/) (2025)
- [Causal Transfer in Medical Image Analysis](https://mlsanity.com/paper/2603.24388/) (2026)
- [The Causal Description Gap: Information-Theoretic Separations Across Pearl's Hierarchy](https://mlsanity.com/paper/2605.02177/) (2026)
- [Certifying Interventional Agreement Among Observationally Equivalent Causal Models](https://mlsanity.com/paper/2609.32247/) (2026)

## Abstract (arXiv)

The aim of this paper is to make clear and precise the relationship between the Rubin causal model (RCM) and structural causal model (SCM) frameworks for causal inference. Adopting a neutral logical perspective, and drawing on previous work, we show what is required for an RCM to be representable by an SCM. A key result then shows that every RCM -- including those that violate algebraic principles implied by the SCM framework -- emerges as an abstraction of some representable RCM. Finally, we illustrate the power of this conciliatory perspective by pinpointing an important role for SCM principles in classic applications of RCMs; conversely, we offer a characterization of the algebraic constraints implied by a graph, helping to substantiate further comparisons between the two frameworks.