# Do Finetti: On Causal Effects for Exchangeable Data

arXiv: https://arxiv.org/abs/2405.18836 · HTML: https://mlsanity.com/paper/2405.18836/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 29 May 2024.

## Builds on (most cited first, 7 of 7)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data](https://mlsanity.com/paper/2203.15756/) (2022)
- [Causal Diagrams for Interference](https://mlsanity.com/paper/1403.1239/) (2014)
- [Detecting hidden confounding in observational data using multiple environments](https://mlsanity.com/paper/2205.13935/) (2022)
- [BRUNO: A Deep Recurrent Model for Exchangeable Data](https://mlsanity.com/paper/1802.07535/) (2018)
- [Energy-Based Processes for Exchangeable Data](https://mlsanity.com/paper/2003.07521/) (2020)

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

- [Do-PFN: In-Context Learning for Causal Effect Estimation](https://mlsanity.com/paper/2506.06039/) (2025)
- [EdgeBench: Unveiling Scaling Laws of Learning from Real-World Environments](https://mlsanity.com/paper/2607.05155/) (2026)
- [Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learning](https://mlsanity.com/paper/2406.14302/) (2024)
- [Counterfactual reasoning: an analysis of in-context emergence](https://mlsanity.com/paper/2506.05188/) (2025)
- [Falsification of Unconfoundedness by Testing Independence of Causal Mechanisms](https://mlsanity.com/paper/2502.06231/) (2025)
- [Superposition Without Interference? Towards Isolated Interventions via Almost Orthogonal Features in Language Models](https://mlsanity.com/paper/2602.04718/) (2026)
- [Infinitesimal Causality](https://mlsanity.com/paper/2606.24621/) (2026)
- [Bayesian Hierarchical Invariant Prediction](https://mlsanity.com/paper/2505.11211/) (2025)
- [On the Emergence and Test-Time Use of Structural Information in Large Language Models](https://mlsanity.com/paper/2601.17869/) (2026)
- [Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach](https://mlsanity.com/paper/2604.05829/) (2026)
- [Estimating Treatment Effects with Independent Component Analysis](https://mlsanity.com/paper/2507.16467/) (2025)

## Abstract (arXiv)

We study causal effect estimation in a setting where the data are not i.i.d. (independent and identically distributed). We focus on exchangeable data satisfying an assumption of independent causal mechanisms. Traditional causal effect estimation frameworks, e.g., relying on structural causal models and do-calculus, are typically limited to i.i.d. data and do not extend to more general exchangeable generative processes, which naturally arise in multi-environment data. To address this gap, we develop a generalized framework for exchangeable data and introduce a truncated factorization formula that facilitates both the identification and estimation of causal effects in our setting. To illustrate potential applications, we introduce a causal P'olya urn model and demonstrate how intervention propagates effects in exchangeable data settings. Finally, we develop an algorithm that performs simultaneous causal discovery and effect estimation given multi-environment data.