# Causal Modeling With Infinitely Many Variables

arXiv: https://arxiv.org/abs/2112.09171 · HTML: https://mlsanity.com/paper/2112.09171/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 28 references that are in the map.
- First posted on arXiv 16 Dec 2021.

## Builds on (most cited first, 4 of 4)

- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [A Modification of the Halpern-Pearl Definition of Causality](https://mlsanity.com/paper/1505.00162/) (2015)
- [On Open-Universe Causal Reasoning](https://mlsanity.com/paper/1907.02170/) (2019)

## Built on by (most cited first, 7 of 7)

- [Gumbel Counterfactual Generation From Language Models](https://mlsanity.com/paper/2411.07180/) (2024)
- [Comparing Causal Frameworks: Potential Outcomes, Structural Models, Graphs, and Abstractions](https://mlsanity.com/paper/2306.14351/) (2023)
- [A Measure-Theoretic Axiomatisation of Causality](https://mlsanity.com/paper/2305.17139/) (2023)
- [Reasoning About Causal Models With Infinitely Many Variables](https://mlsanity.com/paper/2112.11362/) (2021)
- [Causal Models with Constraints](https://mlsanity.com/paper/2301.06845/) (2023)
- [Do Not Marginalize Mechanisms, Rather Consolidate!](https://mlsanity.com/paper/2310.08377/) (2023)
- [Causal Models for Growing Networks](https://mlsanity.com/paper/2504.01012/) (2025)

## Abstract (arXiv)

Structural-equations models (SEMs) are perhaps the most commonly used framework for modeling causality. However, as we show, naively extending this framework to infinitely many variables, which is necessary, for example, to model dynamical systems, runs into several problems. We introduce GSEMs (generalized SEMs), a flexible generalization of SEMs that directly specify the results of interventions, in which (1) systems of differential equations can be represented in a natural and intuitive manner, (2) certain natural situations, which cannot be represented by SEMs at all, can be represented easily, (3) the definition of actual causality in SEMs carries over essentially without change.