Handling Distribution Shifts on Graphs: An Invariance Perspective (2202.02466v5)

Abstract: There is increasing evidence suggesting neural networks' sensitivity to distribution shifts, so that research on out-of-distribution (OOD) generalization comes into the spotlight. Nonetheless, current endeavors mostly focus on Euclidean data, and its formulation for graph-structured data is not clear and remains under-explored, given two-fold fundamental challenges: 1) the inter-connection among nodes in one graph, which induces non-IID generation of data points even under the same environment, and 2) the structural information in the input graph, which is also informative for prediction. In this paper, we formulate the OOD problem on graphs and develop a new invariant learning approach, Explore-to-Extrapolate Risk Minimization (EERM), that facilitates graph neural networks to leverage invariance principles for prediction. EERM resorts to multiple context explorers (specified as graph structure editers in our case) that are adversarially trained to maximize the variance of risks from multiple virtual environments. Such a design enables the model to extrapolate from a single observed environment which is the common case for node-level prediction. We prove the validity of our method by theoretically showing its guarantee of a valid OOD solution and further demonstrate its power on various real-world datasets for handling distribution shifts from artificial spurious features, cross-domain transfers and dynamic graph evolution.

• The paper introduces the EERM method to address out-of-distribution generalization by formulating the OOD problem for graph data.
• It utilizes invariant feature learning with BFS-based ego-graphs to extract stable causal features despite non-IID inter-node dependencies.
• Rigorous theoretical proofs and experiments demonstrate EERM’s superiority over traditional ERM in dynamic, real-world graph scenarios.

Handling Distribution Shifts on Graphs: An Invariance Perspective

The paper "Handling Distribution Shifts on Graphs: An Invariance Perspective" addresses the pressing challenge of out-of-distribution (OOD) generalization specific to graph-structured data. This topic garners significant interest due to the increasing reliance on neural networks, which are known to falter when faced with distribution shifts. Traditional efforts in this domain have largely been confined to Euclidean data, leaving graph data, which presents unique challenges due to its inherent structure and inter-connectivity, relatively under-explored.

The paper introduces the Explore-to-Extrapolate Risk Minimization (EERM) method, aimed at improving OOD generalization for graph neural networks (GNNs). The key contributions of this work are fourfold:

1. Formulation of the OOD Problem for Graphs: The authors propose a novel formulation of the OOD generalization problem in the context of node-level graph prediction tasks. Unlike Euclidean spaces, graph data involves non-independent and non-identically distributed (non-IID) instances due to the inter-connections among nodes. This non-IID nature is a critical factor in graphs, which necessitates a fresh approach in defining the problem.
2. Invariant Feature Learning: By leveraging invariant learning, the method seeks to identify features that remain stable across different environments. The approach involves recursively using the breadth-first search (BFS) tree of ego-graphs, treating nodes within these structures as instances of varying length and permutation. The aim is to extract invariant causal features aiding prediction even when environments change.
3. Theoretical Validation: The paper strengthens its claims with theoretical insights. It shows that EERM guarantees valid OOD solutions by ensuring invariant features in graph data are harnessed for learning. This is supported by rigorous proofs demonstrating that minimizing the variance of risks across different virtual environments can indeed enhance model robustness to distributional shifts.
4. Experimental Validation: Extensive experiments are conducted on a variety of datasets exhibiting different kinds of distribution shifts. These include artificial spurious features, cross-domain graph transfers, and dynamic graph evolution. The results signify EERM's consistent superiority over empirical risk minimization (ERM), with notable improvements in handling novel data distributions in real-world graphs.

The implications of this research are substantial. Practically, robust OOD methods like EERM enhance the applicability of GNNs in dynamic, real-world scenarios where graphs evolve over time or dramatically differ during deployment compared to training data, such as in autonomous driving or fraud detection. Theoretically, this work affirms the need for fresh learning paradigms tailored to graph data, challenging more conventional approaches biased towards Euclidean setups.

Future directions may concentrate on further refining invariant learning mechanisms in GNNs, perhaps by integrating domain adaptation techniques to dynamically adjust to observed shifts during inference, and exploring the scalability of EERM in extremely large graph scenarios. The framework could also be extended to other graph-based learning architectures beyond node-level tasks, potentially influencing insights into graph-level predictions or link prediction challenges.