# Gaussian Processes on Graphs via Spectral Kernel Learning

arXiv: https://arxiv.org/abs/2006.07361 · HTML: https://mlsanity.com/paper/2006.07361/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2020.

## Built on by (most cited first, 24 of 24)

- [Graph Posterior Network: Bayesian Predictive Uncertainty for Node Classification](https://mlsanity.com/paper/2110.14012/) (2021)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Neural Latent Geometry Search: Product Manifold Inference via Gromov-Hausdorff-Informed Bayesian Optimization](https://mlsanity.com/paper/2309.04810/) (2023)
- [Hodge-Compositional Edge Gaussian Processes](https://mlsanity.com/paper/2310.19450/) (2023)
- [Gaussian Processes on Cellular Complexes](https://mlsanity.com/paper/2311.01198/) (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)
- [Linear Transformer Topological Masking with Graph Random Features](https://mlsanity.com/paper/2410.03462/) (2024)
- [Adaptive Batch Sizes for Active Learning A Probabilistic Numerics Approach](https://mlsanity.com/paper/2306.05843/) (2023)
- [Gaussian Processes on Hypergraphs](https://mlsanity.com/paper/2106.01982/) (2021)
- [A Quadrature Approach for General-Purpose Batch Bayesian Optimization via Probabilistic Lifting](https://mlsanity.com/paper/2404.12219/) (2024)
- [Variance-Reducing Couplings for Random Features](https://mlsanity.com/paper/2405.16541/) (2024)
- [Uncertainty Estimation for Heterophilic Graphs Through the Lens of Information Theory](https://mlsanity.com/paper/2505.22152/) (2025)
- [GKNet: Graph Kalman Filtering and Model Inference via Model-based Deep Learning](https://mlsanity.com/paper/2506.22004/) (2025)
- [Evolving-Graph Gaussian Processes](https://mlsanity.com/paper/2106.15127/) (2021)
- [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)
- [Conformalized Gaussian processes for online uncertainty quantification over graphs](https://mlsanity.com/paper/2510.06181/) (2025)
- [Laplacian Kernelized Bandit](https://mlsanity.com/paper/2601.00461/) (2026)
- [GraphMinNet: Learning Dependencies in Graphs with Light Complexity Minimal Architecture](https://mlsanity.com/paper/2502.00282/) (2025)
- [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)
- [On the Impact of Downstream Tasks on Sampling and Reconstructing Noisy Graph Signals](https://mlsanity.com/paper/2509.10874/) (2025)
- [Data-Driven Graph Filters via Adaptive Spectral Shaping](https://mlsanity.com/paper/2602.03698/) (2026)

## Abstract (arXiv)

We propose a graph spectrum-based Gaussian process for prediction of signals defined on nodes of the graph. The model is designed to capture various graph signal structures through a highly adaptive kernel that incorporates a flexible polynomial function in the graph spectral domain. Unlike most existing approaches, we propose to learn such a spectral kernel, where the polynomial setup enables learning without the need for eigen-decomposition of the graph Laplacian. In addition, this kernel has the interpretability of graph filtering achieved by a bespoke maximum likelihood learning algorithm that enforces the positivity of the spectrum. We demonstrate the interpretability of the model in synthetic experiments from which we show the various ground truth spectral filters can be accurately recovered, and the adaptability translates to superior performances in the prediction of real-world graph data of various characteristics.