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Out-Of-Distribution Generalization on Graphs: A Survey

Haoyang Li, Xin Wang, Ziwei Zhang, Wenwu Zhu

TL;DR

This survey tackles the challenge of out-of-distribution generalization for graph-structured data, surveying data-, model-, and learning-strategy–oriented approaches. It formalizes the Graph OOD problem, introduces a three-way taxonomy, and details representative methods in graph data augmentation, disentangled and causal graph representations, invariant learning, adversarial training, and self-supervised learning, complemented by theory and evaluation datasets. The compilation highlights practical strategies for improving robustness under distribution shifts and summarizes theoretical guarantees and benchmarks. It also outlines future directions, including stronger theory, architecture design, environment inference, test-time training, and broader domain applications to guide progress in graph OOD generalization.

Abstract

Graph machine learning has been extensively studied in both academia and industry. Although booming with a vast number of emerging methods and techniques, most of the literature is built on the in-distribution hypothesis, i.e., testing and training graph data are identically distributed. However, this in-distribution hypothesis can hardly be satisfied in many real-world graph scenarios where the model performance substantially degrades when there exist distribution shifts between testing and training graph data. To solve this critical problem, out-of-distribution (OOD) generalization on graphs, which goes beyond the in-distribution hypothesis, has made great progress and attracted ever-increasing attention from the research community. In this paper, we comprehensively survey OOD generalization on graphs and present a detailed review of recent advances in this area. First, we provide a formal problem definition of OOD generalization on graphs. Second, we categorize existing methods into three classes from conceptually different perspectives, i.e., data, model, and learning strategy, based on their positions in the graph machine learning pipeline, followed by detailed discussions for each category. We also review the theories related to OOD generalization on graphs and introduce the commonly used graph datasets for thorough evaluations. Finally, we share our insights on future research directions. This paper is the first systematic and comprehensive review of OOD generalization on graphs, to the best of our knowledge.

Out-Of-Distribution Generalization on Graphs: A Survey

TL;DR

This survey tackles the challenge of out-of-distribution generalization for graph-structured data, surveying data-, model-, and learning-strategy–oriented approaches. It formalizes the Graph OOD problem, introduces a three-way taxonomy, and details representative methods in graph data augmentation, disentangled and causal graph representations, invariant learning, adversarial training, and self-supervised learning, complemented by theory and evaluation datasets. The compilation highlights practical strategies for improving robustness under distribution shifts and summarizes theoretical guarantees and benchmarks. It also outlines future directions, including stronger theory, architecture design, environment inference, test-time training, and broader domain applications to guide progress in graph OOD generalization.

Abstract

Graph machine learning has been extensively studied in both academia and industry. Although booming with a vast number of emerging methods and techniques, most of the literature is built on the in-distribution hypothesis, i.e., testing and training graph data are identically distributed. However, this in-distribution hypothesis can hardly be satisfied in many real-world graph scenarios where the model performance substantially degrades when there exist distribution shifts between testing and training graph data. To solve this critical problem, out-of-distribution (OOD) generalization on graphs, which goes beyond the in-distribution hypothesis, has made great progress and attracted ever-increasing attention from the research community. In this paper, we comprehensively survey OOD generalization on graphs and present a detailed review of recent advances in this area. First, we provide a formal problem definition of OOD generalization on graphs. Second, we categorize existing methods into three classes from conceptually different perspectives, i.e., data, model, and learning strategy, based on their positions in the graph machine learning pipeline, followed by detailed discussions for each category. We also review the theories related to OOD generalization on graphs and introduce the commonly used graph datasets for thorough evaluations. Finally, we share our insights on future research directions. This paper is the first systematic and comprehensive review of OOD generalization on graphs, to the best of our knowledge.
Paper Structure (33 sections, 4 equations, 2 figures, 2 tables)

This paper contains 33 sections, 4 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Definition and Categorization
  3. Problem Definition
  4. Categorization
  5. Data
  6. Structure-wise Graph Data Augmentation
  7. Feature-wise Graph Data Augmentation
  8. Mixed-type Graph Data Augmentation
  9. Model
  10. Disentanglement-based Graph Models
  11. Causality-based Graph Models
  12. Confounder Balancing based Methods
  13. Structural Causal Model based Methods
  14. Counterfactual Inference and Granger Causality based Methods
  15. Learning Strategy
  16. ...and 18 more sections

Figures (2)

  • Figure 1: Complex types of distribution shifts on graphs. The distribution shifts can exist on graph sizes, node features, and graph structural properties li2021ood. The OOD generalized graph approaches are expected to perform well on the unseen testing data even under distribution shifts rather than overfitting the training data.
  • Figure 2: Taxonomy of graph OOD generalization methods. We categorize existing methodologies into three conceptually different branches based on their positions in the graph machine learning pipeline, i.e., data, model and learning strategy.

Theorems & Definitions (1)

  • Definition 1: Graph OOD generalization