Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs (2202.05441v3)

Abstract: Despite recent success in using the invariance principle for out-of-distribution (OOD) generalization on Euclidean data (e.g., images), studies on graph data are still limited. Different from images, the complex nature of graphs poses unique challenges to adopting the invariance principle. In particular, distribution shifts on graphs can appear in a variety of forms such as attributes and structures, making it difficult to identify the invariance. Moreover, domain or environment partitions, which are often required by OOD methods on Euclidean data, could be highly expensive to obtain for graphs. To bridge this gap, we propose a new framework, called Causality Inspired Invariant Graph LeArning (CIGA), to capture the invariance of graphs for guaranteed OOD generalization under various distribution shifts. Specifically, we characterize potential distribution shifts on graphs with causal models, concluding that OOD generalization on graphs is achievable when models focus only on subgraphs containing the most information about the causes of labels. Accordingly, we propose an information-theoretic objective to extract the desired subgraphs that maximally preserve the invariant intra-class information. Learning with these subgraphs is immune to distribution shifts. Extensive experiments on 16 synthetic or real-world datasets, including a challenging setting -- DrugOOD, from AI-aided drug discovery, validate the superior OOD performance of CIGA.

• The paper presents CIGA, a framework that leverages structural causal models to identify invariant graph substructures.
• It employs an information-theoretic contrastive learning approach to robustly capture essential features across distribution shifts.
• Extensive evaluation demonstrates significant improvements in OOD generalization on diverse datasets, including applications in AI-driven drug discovery.

Learning Causally Invariant Representations for Out-of-Distribution Generalization on Graphs

The paper presents a novel framework, referred to as CIGA, aimed at enhancing out-of-distribution (OOD) generalization for graph data. Unlike Euclidean data where the invariance principle has seen considerable success, applying this principle to graphs is challenging due to the complexity of graph data and the diverse nature of distribution shifts they can undergo. However, graphs often don't come with predefined domain labels, which makes traditional OOD methods less applicable.

Key Contributions

1. Causal Modeling of Graph Data: The authors employed structural causal models (SCMs) to represent distribution shifts within graph data. This involves characterizing the invariant and spurious features across possible environments, thereby making it feasible to identify causally invariant parts of the graphs.
2. Framework for Causal Invariance: The CIGA framework is designed to learn graph representations that remain stable across different distributions. This is achieved by focusing mainly on subgraphs that encapsulate intrinsically causal information regarding the labels.
3. Information-Theoretic Objective: An information-theoretic approach is proposed to extract these subgraphs, thus preserving essential intra-class information. CIGA leverages contrastive learning to approximate mutual information, enhancing the identification of the invariant substructures.
4. Extensive Evaluation: The framework is evaluated extensively across several datasets comprising both synthetic and real-world graphs, including those from AI-driven drug discovery scenarios. The results showcased significant improvements in OOD generalization over existing methods.

Empirical and Theoretical Insights

Robust and Flexible OOD Generalization:

The CIGA framework demonstrated superior performance in OOD scenarios by showing its ability to navigate complex distribution shifts effectively. Notably, the paper illustrates that even when confronted with joint shifts in graph topology and node features, the proposed model outperforms other architectures and optimization objectives.

Applicability to Diverse Graph Types:

The mathematical foundation, particularly the causal models used in this paper, is generalizable to an assortment of graph families, reflecting a broad applicability across domains with varying graph characteristics, from simple structures to complex heterogeneous networks.

Optimization Efficiency:

Paramount to the CIGA framework's effectiveness is its reliance on graph neural network (GNN) architectures that disassemble into separate modules, fostering algorithmic alignment with causally directed processes inherent to graph data. This decomposition is key to handling invariant and non-invariant parts of the graph data diligently.

Theoretical Guarantees:

In-depth theoretical analysis justifies the framework's capacity to provably identify underlying invariant subgraphs, which are vital for scale and translate beyond training environments. The paper underscores the framework’s robustness by rigorously analyzing the limitations and strengths under diverse graph generation conditions.

Future Directions

The introduction of CIGA opens several pathways for future investigation, including refining graph generation models to incorporate domain-specific knowledge, developing sophisticated sampling strategies for contrastive learning, and exploring alternative architectures for broader applicability. Additionally, extensions to node-level classification and further exploration of training strategies in single-environment setups present opportunities to expand on the framework's foundational insights. The potential for improved optimization techniques tailored for OOD settings also remains an appealing direction for further innovation.

Overall, the research takes a pivotal step forward in enhancing the generalization ability of GNNs across diverse and shifting data landscapes, underscoring the necessity of causal reasoning in the design of more robust graph learning models.