# Gaussian Processes Over Graphs

arXiv: https://arxiv.org/abs/1803.05776 · HTML: https://mlsanity.com/paper/1803.05776/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2018.

## Built on by (most cited first, 14 of 14)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Hodge-Compositional Edge Gaussian Processes](https://mlsanity.com/paper/2310.19450/) (2023)
- [Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets](https://mlsanity.com/paper/2110.12752/) (2021)
- [Bayesian Optimisation of Functions on Graphs](https://mlsanity.com/paper/2306.05304/) (2023)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Scalable Deep Gaussian Markov Random Fields for General Graphs](https://mlsanity.com/paper/2206.05032/) (2022)
- [Evolving-Graph Gaussian Processes](https://mlsanity.com/paper/2106.15127/) (2021)
- [Dynamic Bayesian Learning for Spatiotemporal Mechanistic Models](https://mlsanity.com/paper/2208.06528/) (2022)
- [Transductive Kernels for Gaussian Processes on Graphs](https://mlsanity.com/paper/2211.15322/) (2022)
- [Learning signals defined on graphs with optimal transport and Gaussian process regression](https://mlsanity.com/paper/2410.15721/) (2024)
- [Laplacian Kernelized Bandit](https://mlsanity.com/paper/2601.00461/) (2026)
- [A Review of Graph-Powered Data Quality Applications for IoT Monitoring Sensor Networks](https://mlsanity.com/paper/2410.21006/) (2024)
- [Low-rank computation of the posterior mean in Multi-Output Gaussian Processes](https://mlsanity.com/paper/2504.21527/) (2025)
- [Multi-Output Gaussian Processes for Graph-Structured Data](https://mlsanity.com/paper/2505.16755/) (2025)

## Abstract (arXiv)

We propose Gaussian processes for signals over graphs (GPG) using the apriori knowledge that the target vectors lie over a graph. We incorporate this information using a graph- Laplacian based regularization which enforces the target vectors to have a specific profile in terms of graph Fourier transform coeffcients, for example lowpass or bandpass graph signals. We discuss how the regularization affects the mean and the variance in the prediction output. In particular, we prove that the predictive variance of the GPG is strictly smaller than the conventional Gaussian process (GP) for any non-trivial graph. We validate our concepts by application to various real-world graph signals. Our experiments show that the performance of the GPG is superior to GP for small training data sizes and under noisy training.