Online Bayesian Node Classification on Inductive Graphs under Distribution Shift

Abstract:On evolving graphs, node classifiers must satisfy two key requirements: inductive generalization to newly arriving nodes under distribution shift and calibrated uncertainty for safety-sensitive applications. Standard graph neural networks (GNNs) are typically trained once and address neither requirement. We adapt the Bayesian last-layer (BLL) model by placing random last-layer parameters on top of a deterministic GNN encoder for uncertainty quantification. The categorical softmax likelihood required for classification breaks Gaussian conjugacy, so neither the training posterior nor the test-time streaming update has a closed-form solution. To address both challenges, we introduce a variational Bayesian last-layer (VBLL) objective that jointly trains the encoder and an approximate last-layer posterior by maximizing an evidence lower bound with a Monte Carlo expected log-likelihood. At test time, we freeze the encoder and apply an online Laplace update to the last-layer posterior. This update corresponds to a power-prior Bayesian model with exponential forgetting and a Kullback-Leibler anchor to the training posterior. Across five node-classification benchmarks under distribution shift, online GVBLL is the only method to achieve the best accuracy and negative log-likelihood on every dataset. It improves accuracy by up to 17 percentage points on Cora and 14 percentage points on ogbn-arxiv over the strongest non-GVBLL baseline, while remaining competitive in calibration with MC Dropout, Deep Ensembles, Temperature Scaling, and Gaussian-process classifiers.

Machine Learning (cs.LG); Methodology (stat.ME); Machine Learning (stat.ML)

arXiv:2609.13655 [cs.LG]

(or arXiv:2609.13655v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.13655 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.