Measure-Theoretic Anti-Causal Representation Learning

TL;DR

This paper introduces ACIA, a measure-theoretic framework for anti-causal representation learning that captures stable causal patterns across environments, improving out-of-distribution generalization in complex data.

Contribution

ACIA is a novel measure-theoretic approach that handles imperfect interventions, high-dimensional data, and provides theoretical guarantees without relying on explicit causal structures.

Findings

ACIA outperforms state-of-the-art methods in accuracy and invariance.

Theoretical bounds on performance gaps between training and unseen environments.

Effective in synthetic and real-world medical datasets.

Abstract

Causal representation learning in the anti-causal setting (labels cause features rather than the reverse) presents unique challenges requiring specialized approaches. We propose Anti-Causal Invariant Abstractions (ACIA), a novel measure-theoretic framework for anti-causal representation learning. ACIA employs a two-level design, low-level representations capture how labels generate observations, while high-level representations learn stable causal patterns across environment-specific variations. ACIA addresses key limitations of existing approaches by accommodating prefect and imperfect interventions through interventional kernels, eliminating dependency on explicit causal structures, handling high-dimensional data effectively, and providing theoretical guarantees for out-of-distribution generalization. Experiments on synthetic and real-world medical datasets demonstrate that ACIA consistently outperforms state-of-the-art methods in both accuracy and invariance metrics. Furthermore, our theoretical results establish tight bounds on performance gaps between training and unseen environments, confirming the efficacy of our approach for robust anti-causal learning.