Conceptual Relationship Between Classical Machine Learning and Graph Neural Networks in Out-of-Distribution Detection: A Comprehensive Survey
Out-of-Distribution (OOD) detection, an important branch of Anomaly Detection (AD), aims to recognize inputs that fall outside the training distribution. Existing OOD methods based on statistical modeling, distance measures, one-class classification, reconstruction, or energy-based scoring provide strong foundations, but they can be difficult to apply directly to high-dimensional, unstructured, or relational data. Recent advances in graph-based deep learning, particularly Graph Neural Networks (GNNs), create new opportunities by modeling local and global dependencies among interdependent samples. This survey provides a comprehensive overview of OOD detection methods, organizing them into traditional and deep learning families before examining graph-aware GNN-based approaches. Beyond taxonomy, we synthesize the conceptual relationships between these paradigms through three working hypotheses: graph-aware transfer, structure-sensitive scoring, and hybrid objective design. This hypothesis-guided synthesis characterizes how established statistical, geometric, reconstruction-based, and energy-based principles can be transferred, reformulated, and combined within modern GNN frameworks. To make this perspective concrete, we include Graph Energy-based OOD Detection (GEO), a reference case study that combines energy-based scoring with one-class regularization in a GNN architecture and reports competitive but setting-dependent performance across representative benchmarks. Taken together, the survey clarifies the current landscape of OOD detection and highlights how integrating classical statistical reasoning with graph-based learning can inform future graph OOD research. To support reproducibility, the implementation of GEO is publicly available at https://github.com/longstnguyen/GEO.