# Distributionally Robust Causal Abstractions

arXiv: https://arxiv.org/abs/2510.04842 · HTML: https://mlsanity.com/paper/2510.04842/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 6 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Causal Abstractions of Neural Networks](https://mlsanity.com/paper/2106.02997/) (2021)
- [Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning](https://mlsanity.com/paper/1908.08729/) (2019)
- [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)
- [Compositional Abstraction Error and a Category of Causal Models](https://mlsanity.com/paper/2103.15758/) (2021)
- [Jointly Learning Consistent Causal Abstractions Over Multiple Interventional Distributions](https://mlsanity.com/paper/2301.05893/) (2023)
- [Neural Causal Abstractions](https://mlsanity.com/paper/2401.02602/) (2024)
- [Targeted Reduction of Causal Models](https://mlsanity.com/paper/2311.18639/) (2023)
- [Robust and Conjugate Gaussian Process Regression](https://mlsanity.com/paper/2311.00463/) (2023)
- [Causal Optimal Transport of Abstractions](https://mlsanity.com/paper/2312.08107/) (2023)
- [Learning Causal Abstractions of Linear Structural Causal Models](https://mlsanity.com/paper/2406.00394/) (2024)
- [Mean-Covariance Robust Risk Measurement](https://mlsanity.com/paper/2112.09959/) (2021)
- [Causal Abstraction Learning based on the Semantic Embedding Principle](https://mlsanity.com/paper/2502.00407/) (2025)
- [Causally Abstracted Multi-armed Bandits](https://mlsanity.com/paper/2404.17493/) (2024)
- [Aligning Graphical and Functional Causal Abstractions](https://mlsanity.com/paper/2412.17080/) (2024)
- [Towards Computing an Optimal Abstraction for Structural Causal Models](https://mlsanity.com/paper/2208.00894/) (2022)
- [Generative Intervention Models for Causal Perturbation Modeling](https://mlsanity.com/paper/2411.14003/) (2024)

## Built on by (most cited first, 3 of 3)

- [Coarsening Causal DAG Models](https://mlsanity.com/paper/2601.10531/) (2026)
- [Causal Representation Learning for Generalisable Recommendation](https://mlsanity.com/paper/2605.27043/) (2026)
- [Score-Based Learning of Cluster DAGs from Interventions](https://mlsanity.com/paper/2610.11947/) (2026)

## Abstract (arXiv)

Causal Abstraction (CA) theory provides a principled framework for relating causal models that describe the same system at different levels of granularity while ensuring interventional consistency between them. Recent methods for learning CAs, however, assume fixed and well-specified exogenous distributions, leaving them vulnerable to environmental shifts and model misspecification. In this work, we address these limitations by introducing the first class of distributionally robust CAs and their associated learning algorithms. The latter cast robust causal abstraction learning as a constrained min-max optimization problem with Wasserstein ambiguity sets. We provide theoretical guarantees for both empirical and Gaussian environments, enabling principled selection of ambiguity set radii and establish quantitative guarantees on worst-case abstraction error. Furthermore, we present empirical evidence across different problems and CA learning methods, demonstrating our framework's robustness not only to environmental shifts but also to structural and intervention mapping misspecification.