Measure-Theoretic Anti-Causal Representation Learning

2025-10-16

AI Summary

Anticausal representation learning confronts out-of-distribution (OOD) generalization challenges arising when labels generate features—not vice versa. To address this, we propose the Anticausal Invariant Architecture (ACIA): a measure-theoretic framework that models anticausal generative mechanisms, employing an intervention kernel to uniformly handle both perfect and imperfect interventions—thereby eliminating reliance on explicit causal graphs. ACIA adopts a two-tiered representation architecture: the lower tier captures the label-driven observational generation process, while the upper tier extracts environment-invariant causal patterns, enhanced by invariance regularization and representation disentanglement for robust learning. Theoretically, we derive a tight bound on the OOD generalization performance gap. Empirically, ACIA achieves significant improvements in accuracy and invariance metrics on both synthetic and real-world medical datasets, validating its effectiveness and theoretical guarantees.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

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.

Problem

• Developing anti-causal representation learning where labels cause features
• Learning stable causal patterns across environmental variations
• Providing theoretical guarantees for out-of-distribution generalization

Innovation

• Two-level design captures label-observation generation process
• Uses interventional kernels for perfect and imperfect interventions
• Provides theoretical guarantees for out-of-distribution generalization