# Meaningful Causal Aggregation and Paradoxical Confounding

arXiv: https://arxiv.org/abs/2304.11625 · HTML: https://mlsanity.com/paper/2304.11625/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 23 Apr 2023.

## Builds on (most cited first, 11 of 11)

- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Causal Consistency of Structural Equation Models](https://mlsanity.com/paper/1707.00819/) (2017)
- [Abstracting Causal Models](https://mlsanity.com/paper/1812.03789/) (2018)
- [Approximate Causal Abstraction](https://mlsanity.com/paper/1906.11583/) (2019)
- [Assaying Out-Of-Distribution Generalization in Transfer Learning](https://mlsanity.com/paper/2207.09239/) (2022)
- [backShift: Learning causal cyclic graphs from unknown shift interventions](https://mlsanity.com/paper/1506.02494/) (2015)
- [Compositional Abstraction Error and a Category of Causal Models](https://mlsanity.com/paper/2103.15758/) (2021)
- [Multi-Level Cause-Effect Systems](https://mlsanity.com/paper/1512.07942/) (2015)
- [Causal Abstraction with Soft Interventions](https://mlsanity.com/paper/2211.12270/) (2022)
- [Phenomenological Causality](https://mlsanity.com/paper/2211.09024/) (2022)
- [Causal Models with Constraints](https://mlsanity.com/paper/2301.06845/) (2023)

## Built on by (most cited first, 5 of 5)

- [Targeted Reduction of Causal Models](https://mlsanity.com/paper/2311.18639/) (2023)
- [What is causal about causal models and representations?](https://mlsanity.com/paper/2501.19335/) (2025)
- [Cluster-Dags as Powerful Background Knowledge For Causal Discovery](https://mlsanity.com/paper/2512.10032/) (2025)
- [Lost in Aggregation: The Causal Interpretation of the IV Estimand](https://mlsanity.com/paper/2601.12120/) (2026)
- [Formalizing and falsifying causal pathways of rare events](https://mlsanity.com/paper/2605.31254/) (2026)

## Abstract (arXiv)

In aggregated variables the impact of interventions is typically ill-defined because different micro-realizations of the same macro-intervention can result in different changes of downstream macro-variables. We show that this ill-definedness of causality on aggregated variables can turn unconfounded causal relations into confounded ones and vice versa, depending on the respective micro-realization. We argue that it is practically infeasible to only use aggregated causal systems when we are free from this ill-definedness. Instead, we need to accept that macro causal relations are typically defined only with reference to the micro states. On the positive side, we show that cause-effect relations can be aggregated when the macro interventions are such that the distribution of micro states is the same as in the observational distribution; we term this natural macro interventions. We also discuss generalizations of this observation.