Distributionally Robust Causal Abstractions
This work addresses robustness issues in causal abstraction learning for AI and causal inference, representing an incremental improvement over prior methods.
The paper tackles the vulnerability of existing causal abstraction learning methods to environmental shifts and misspecification by introducing the first class of distributionally robust causal abstractions and associated learning algorithms, demonstrating robustness across different problems and methods.
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. Recently, several approaches for learning CAs have been proposed, but all assume fixed and well-specified exogenous distributions, making them vulnerable to environmental shifts and 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 results, for both empirical and Gaussian environments, leading to principled selection of the level of robustness via the radius of these sets. 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 model and intervention mapping misspecification.