Unifying Causal Representation Learning with the Invariance Principle (2409.02772v2)

Abstract: Causal representation learning (CRL) aims at recovering latent causal variables from high-dimensional observations to solve causal downstream tasks, such as predicting the effect of new interventions or more robust classification. A plethora of methods have been developed, each tackling carefully crafted problem settings that lead to different types of identifiability. These different settings are widely assumed to be important because they are often linked to different rungs of Pearl's causal hierarchy, even though this correspondence is not always exact. This work shows that instead of strictly conforming to this hierarchical mapping, many causal representation learning approaches methodologically align their representations with inherent data symmetries. Identification of causal variables is guided by invariance principles that are not necessarily causal. This result allows us to unify many existing approaches in a single method that can mix and match different assumptions, including non-causal ones, based on the invariance relevant to the problem at hand. It also significantly benefits applicability, which we demonstrate by improving treatment effect estimation on real-world high-dimensional ecological data. Overall, this paper clarifies the role of causal assumptions in the discovery of causal variables and shifts the focus to preserving data symmetries.

• The paper presents a unified invariant framework that explains multiple causal representation learning methods by aligning latent variables with observed invariances.
• It establishes theoretical identifiability results by enforcing sufficiency and invariance constraints, ensuring robust causal discovery.
• The framework demonstrates improved treatment effect estimation on high-dimensional ecological data, bridging theory with practical applications.

Unifying Causal Representation Learning with the Invariance Principle

The paper "Unifying Causal Representation Learning with the Invariance Principle" by Dingling Yao et al. addresses the field of causal representation learning (CRL), which seeks to discover latent causal structures from high-dimensional observational data. The authors analyze the landscape of CRL methods and propose a unifying framework based on the invariance principle, arguing that many existing CRL approaches can be understood through this lens.

Problem Context

Causal representation learning aims to identify interpretable and low-dimensional latent causal variables and their relationships from high-dimensional data. These latent variables can improve the robustness of models under distribution shifts and enhance the reliability of predictions and interventions. The challenge lies in guaranteeing the identifiability of these latent variables and their causal structures.

Key Contributions

1. Unified Framework: The authors propose a unifying perspective that connects various CRL methods through the concept of invariance. They suggest that many CRL methods align representations based on known data symmetries, even if these symmetries are not necessarily causal.
2. Equivalence Classes and Invariances: The paper demonstrates that CRL methods often identify latent variables by considering equivalence classes across different "data pockets" that exhibit certain invariances. This allows for mixing different assumptions, including non-causal ones, depending on the application.
3. Improved Applicability: By framing CRL through the invariance principle, the authors show how their approach can enhance treatment effect estimation using real-world high-dimensional ecological data.
4. Identifiability Results: They extend the theoretical understanding of identifiability in CRL, showing that it can be achieved by enforcing both sufficiency (preserving information about the observations) and invariance constraints.

Theoretical Insights

The authors formalize the problem by introducing the notion of invariant properties and equivalence relations. Their framework identifies latent variables by ensuring that the learned representation aligns with invariances present in the data. They define sufficiency and invariance constraints and prove that these constraints lead to block-identifiability of the latent variables.

Definitions and Assumptions

• Invariant Properties: A property that maps latent variables to a space where invariance holds, ensuring that transformations preserving some subsets do not apply to others.
• Encoders and Selectors: Functions that map observations to latent representations, with selectors isolating components relevant to different invariance properties.

Practical and Theoretical Implications

The paper's framework clarifies and unifies various CRL methodologies, providing a solid foundation for future research. By focusing on invariance, researchers can tailor assumptions to specific applications, facilitating more flexible and robust CRL methods. The framework also highlights the conditions under which latent variables and causal graphs can be identified, contributing to a deeper theoretical understanding of CRL.

Numerical Results and Bold Claims

The authors demonstrate the effectiveness of their approach with quantitative results showing improved treatment effect estimation on ecological data. They also present synthetic ablations illustrating that non-trivial distributional invariances, rather than strict causal interventions, are crucial for identifiability.

Future Directions

The authors speculate on future developments in AI and CRL, suggesting that the invariance principle could bridge gaps between CRL and other fields like domain adaptation and geometric deep learning. They also highlight emerging research areas, such as learning representations from multiple data distributions and enhancing the practical applicability of CRL methods.

Related Work and Broader Research Context

The paper revisits various CRL approaches, framing them as special cases of their invariance-based theory. They compare methods from multiview CRL, multi-environment CRL, temporal CRL, multi-task CRL, and domain generalization, showing how these methods align with their framework.

Conclusion

"Unifying Causal Representation Learning with the Invariance Principle" offers a comprehensive and insightful look at the coherence among different CRL methods through the invariance principle. This perspective not only enhances the theoretical foundation of CRL but also has practical implications for designing robust and flexible CRL algorithms. Through careful analysis and extensive theoretical backing, the authors provide a valuable contribution that is likely to shape future research in the field.