{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13655",
  "author_total": 3,
  "authors": [
    {
      "name": "Jinwen Xu"
    },
    {
      "name": "Gonzalo Mateos Buckstein"
    },
    {
      "name": "Qin Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bvdswf45gevq1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13655",
  "fulltext_url": null,
  "id": "bvdswf45gevq1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13655",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Advanced Graph Neural Networks"
    ]
  ],
  "openalex": "W7213338932",
  "pdf_url": "https://arxiv.org/pdf/2609.13655",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bvdswf45gevq1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:36Z",
      "native_id": "2609.13655",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13655"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Online Bayesian Node Classification on Inductive Graphs under Distribution Shift",
  "title_text": "Online Bayesian Node Classification on Inductive Graphs under Distribution Shift",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:36Z",
  "url": "https://research.draconitic.com/paper/bvdswf45gevq1",
  "venue": "arXiv",
  "versions": []
}