Energy-based Out-of-Distribution Detection for Graph Neural Networks

Learning on graphs, where instance nodes are inter-connected, has become one of the central problems for deep learning, as relational structures are pervasive and induce data inter-dependence which hinders trivial adaptation of existing approaches that assume inputs to be i.i.d. sampled. However, current models mostly focus on improving testing performance of in-distribution data and largely ignore the potential risk w.r.t. out-of-distribution (OOD) testing samples that may cause negative outcome if the prediction is overconfident on them. In this paper, we investigate the under-explored problem, OOD detection on graph-structured data, and identify a provably effective OOD discriminator based on an energy function directly extracted from graph neural networks trained with standard classification loss. This paves a way for a simple, powerful and efficient OOD detection model for GNN-based learning on graphs, which we call GNNSAFE. It also has nice theoretical properties that guarantee an overall distinguishable margin between the detection scores for in-distribution and OOD samples, which, more critically, can be further strengthened by a learning-free energy belief propagation scheme. For comprehensive evaluation, we introduce new benchmark settings that evaluate the model for detecting OOD data from both synthetic and real distribution shifts (crossdomain graph shifts and temporal graph shifts). The results show that GNNSAFE achieves up to 17.0% AUROC improvement over state-of-the-arts and it could serve as simple yet strong baselines in such an under-developed area. The codes are available at https://github.com/qitianwu/GraphOOD-GNNSafe .