# Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data

arXiv: https://arxiv.org/abs/2203.15756 · HTML: https://mlsanity.com/paper/2203.15756/

## Key facts

- Cited by 42 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 58 references that are in the map.
- First posted on arXiv 29 Mar 2022.

## Builds on (most cited first, 18 of 18)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [Recurrent Independent Mechanisms](https://mlsanity.com/paper/1909.10893/) (2019)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [Learning Independent Causal Mechanisms](https://mlsanity.com/paper/1712.00961/) (2017)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [Causal Discovery with General Non-Linear Relationships Using Non-Linear ICA](https://mlsanity.com/paper/1904.09096/) (2019)
- [Causal Discovery from Changes](https://mlsanity.com/paper/1301.2312/) (2013)
- [Fast and Slow Learning of Recurrent Independent Mechanisms](https://mlsanity.com/paper/2105.08710/) (2021)
- [Group invariance principles for causal generative models](https://mlsanity.com/paper/1705.02212/) (2017)

## Built on by (most cited first, 30 of 42)

- [Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis](https://mlsanity.com/paper/2206.02013/) (2022)
- [Do-PFN: In-Context Learning for Causal Effect Estimation](https://mlsanity.com/paper/2506.06039/) (2025)
- [Object Representations as Fixed Points: Training Iterative Refinement Algorithms with Implicit Differentiation](https://mlsanity.com/paper/2207.00787/) (2022)
- [Provably Learning Object-Centric Representations](https://mlsanity.com/paper/2305.14229/) (2023)
- [Position: Understanding LLMs Requires More Than Statistical Generalization](https://mlsanity.com/paper/2405.01964/) (2024)
- [Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learning](https://mlsanity.com/paper/2406.14302/) (2024)
- [Detecting hidden confounding in observational data using multiple environments](https://mlsanity.com/paper/2205.13935/) (2022)
- [Bivariate Causal Discovery using Bayesian Model Selection](https://mlsanity.com/paper/2306.02931/) (2023)
- [Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environment](https://mlsanity.com/paper/2406.13371/) (2024)
- [Do Finetti: On Causal Effects for Exchangeable Data](https://mlsanity.com/paper/2405.18836/) (2024)
- [An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis](https://mlsanity.com/paper/2311.18048/) (2023)
- [Causality is Key for Interpretability Claims to Generalise](https://mlsanity.com/paper/2602.16698/) (2026)
- [Non-parametric identifiability and sensitivity analysis of synthetic control models](https://mlsanity.com/paper/2301.07656/) (2023)
- [On the Interventional Kullback-Leibler Divergence](https://mlsanity.com/paper/2302.05380/) (2023)
- [AI for Science: An Emerging Agenda](https://mlsanity.com/paper/2303.04217/) (2023)
- [Dataflow graphs as complete causal graphs](https://mlsanity.com/paper/2303.09552/) (2023)
- [Intuitionistic j-Do-Calculus in Topos Causal Models](https://mlsanity.com/paper/2510.17944/) (2025)
- [SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamics](https://mlsanity.com/paper/2302.03663/) (2023)
- [Out-of-Variable Generalization for Discriminative Models](https://mlsanity.com/paper/2304.07896/) (2023)
- [Multi-Domain Causal Discovery in Bijective Causal Models](https://mlsanity.com/paper/2504.21261/) (2025)
- [Counterfactual reasoning: an analysis of in-context emergence](https://mlsanity.com/paper/2506.05188/) (2025)
- [Causal Discovery via Quantile Partial Effect](https://mlsanity.com/paper/2509.12981/) (2025)
- [Conditionally Invariant Representation Learning for Disentangling Cellular Heterogeneity](https://mlsanity.com/paper/2307.00558/) (2023)
- [Detecting and Measuring Confounding Using Causal Mechanism Shifts](https://mlsanity.com/paper/2409.17840/) (2024)
- [Falsification of Unconfoundedness by Testing Independence of Causal Mechanisms](https://mlsanity.com/paper/2502.06231/) (2025)
- [Learning with Hidden Factorial Structure](https://mlsanity.com/paper/2411.01375/) (2024)
- [Probabilistic Modelling is Sufficient for Causal Inference](https://mlsanity.com/paper/2512.23408/) (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)
- [PerturbPFN: Probing the Limits of Synthetic Priors in Drug Perturbation Modelling](https://mlsanity.com/paper/2607.23447/) (2026)

## Abstract (arXiv)

Constraint-based causal discovery methods leverage conditional independence tests to infer causal relationships in a wide variety of applications. Just as the majority of machine learning methods, existing work focuses on studying textitindependent and identically distributed data. However, it is known that even with infinite i.i.d.  data, constraint-based methods can only identify causal structures up to broad Markov equivalence classes, posing a fundamental limitation for causal discovery. In this work, we observe that exchangeable data contains richer conditional independence structure than i.i.d.  data, and show how the richer structure can be leveraged for causal discovery. We first present causal de Finetti theorems, which state that exchangeable distributions with certain non-trivial conditional independences can always be represented as textitindependent causal mechanism (ICM) generative processes. We then present our main identifiability theorem, which shows that given data from an ICM generative process, its unique causal structure can be identified through performing conditional independence tests. We finally develop a causal discovery algorithm and demonstrate its applicability to inferring causal relationships from multi-environment data. Our code and models are publicly available at: https://github.com/syguo96/Causal-de-Finetti