Causal Optimal Transport of Abstractions

TL;DR

This paper introduces COTA, a novel method that learns causal abstraction maps directly from observational and interventional data using optimal transport, enabling causal reasoning across different models without full SCM knowledge.

Contribution

COTA is the first approach to learn causal abstraction maps from data without assuming complete SCM information, integrating do-calculus constraints with optimal transport.

Findings

COTA outperforms non-causal methods on synthetic and real data.

It effectively links interventions across multiple SCMs.

Demonstrates utility as a data augmentation tool.

Abstract

Causal abstraction (CA) theory establishes formal criteria for relating multiple structural causal models (SCMs) at different levels of granularity by defining maps between them. These maps have significant relevance for real-world challenges such as synthesizing causal evidence from multiple experimental environments, learning causally consistent representations at different resolutions, and linking interventions across multiple SCMs. In this work, we propose COTA, the first method to learn abstraction maps from observational and interventional data without assuming complete knowledge of the underlying SCMs. In particular, we introduce a multi-marginal Optimal Transport (OT) formulation that enforces do-calculus causal constraints, together with a cost function that relies on interventional information. We extensively evaluate COTA on synthetic and real world problems, and showcase its advantages over non-causal, independent and aggregated COTA formulations. Finally, we demonstrate the efficiency of our method as a data augmentation tool by comparing it against the state-of-the-art CA learning framework, which assumes fully specified SCMs, on a real-world downstream task.