# Bayesian Semi-supervised Learning with Graph Gaussian Processes

arXiv: https://arxiv.org/abs/1809.04379 · HTML: https://mlsanity.com/paper/1809.04379/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2018.

## Built on by (most cited first, 28 of 28)

- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [NP-Match: When Neural Processes meet Semi-Supervised Learning](https://mlsanity.com/paper/2207.01066/) (2022)
- [Noise-robust Graph Learning by Estimating and Leveraging Pairwise Interactions](https://mlsanity.com/paper/2106.07451/) (2021)
- [Semi-relaxed Gromov-Wasserstein divergence with applications on graphs](https://mlsanity.com/paper/2110.02753/) (2021)
- [Template based Graph Neural Network with Optimal Transport Distances](https://mlsanity.com/paper/2205.15733/) (2022)
- [JuryGCN: Quantifying Jackknife Uncertainty on Graph Convolutional Networks](https://mlsanity.com/paper/2210.05959/) (2022)
- [Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets](https://mlsanity.com/paper/2110.12752/) (2021)
- [Safety in Graph Machine Learning: Threats and Safeguards](https://mlsanity.com/paper/2405.11034/) (2024)
- [Approximately Bayes-Optimal Pseudo Label Selection](https://mlsanity.com/paper/2302.08883/) (2023)
- [Training on Test Data with Bayesian Adaptation for Covariate Shift](https://mlsanity.com/paper/2109.12746/) (2021)
- [Bayesian Optimisation of Functions on Graphs](https://mlsanity.com/paper/2306.05304/) (2023)
- [Graph Neural Networks Do Not Always Oversmooth](https://mlsanity.com/paper/2406.02269/) (2024)
- [Graph Neural Network-Inspired Kernels for Gaussian Processes in Semi-Supervised Learning](https://mlsanity.com/paper/2302.05828/) (2023)
- [Hida-Mat'ern Kernel](https://mlsanity.com/paper/2107.07098/) (2021)
- [Dimensionality Reduction as Probabilistic Inference](https://mlsanity.com/paper/2304.07658/) (2023)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [DisenSemi: Semi-supervised Graph Classification via Disentangled Representation Learning](https://mlsanity.com/paper/2407.14081/) (2024)
- [Uncertainty Propagation in Node Classification](https://mlsanity.com/paper/2304.00918/) (2023)
- [Uncertainty Estimation for Heterophilic Graphs Through the Lens of Information Theory](https://mlsanity.com/paper/2505.22152/) (2025)
- [Evolving-Graph Gaussian Processes](https://mlsanity.com/paper/2106.15127/) (2021)
- [Relational VAE: A Continuous Latent Variable Model for Graph Structured Data](https://mlsanity.com/paper/2106.16049/) (2021)
- [Transductive Kernels for Gaussian Processes on Graphs](https://mlsanity.com/paper/2211.15322/) (2022)
- [NP-Match: Towards a New Probabilistic Model for Semi-Supervised Learning](https://mlsanity.com/paper/2301.13569/) (2023)
- [Conformalized Gaussian processes for online uncertainty quantification over graphs](https://mlsanity.com/paper/2510.06181/) (2025)
- [In all LikelihoodS: How to Reliably Select Pseudo-Labeled Data for Self-Training in Semi-Supervised Learning](https://mlsanity.com/paper/2303.01117/) (2023)
- [Multiple-Source Localization from a Single-Snapshot Observation Using Graph Bayesian Optimization](https://mlsanity.com/paper/2403.16818/) (2024)
- [GraphPPD: Posterior Predictive Modelling for Graph-Level Inference](https://mlsanity.com/paper/2508.16995/) (2025)
- [Two Birds with One Stone: Enhancing Uncertainty Quantification and Interpretability with Graph Functional Neural Process](https://mlsanity.com/paper/2508.17097/) (2025)

## Abstract (arXiv)

We propose a data-efficient Gaussian process-based Bayesian approach to the semi-supervised learning problem on graphs. The proposed model shows extremely competitive performance when compared to the state-of-the-art graph neural networks on semi-supervised learning benchmark experiments, and outperforms the neural networks in active learning experiments where labels are scarce. Furthermore, the model does not require a validation data set for early stopping to control over-fitting. Our model can be viewed as an instance of empirical distribution regression weighted locally by network connectivity. We further motivate the intuitive construction of the model with a Bayesian linear model interpretation where the node features are filtered by an operator related to the graph Laplacian. The method can be easily implemented by adapting off-the-shelf scalable variational inference algorithms for Gaussian processes.