# Graph Convolutional Gaussian Processes

arXiv: https://arxiv.org/abs/1905.05739 · HTML: https://mlsanity.com/paper/1905.05739/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2019.

## Built on by (most cited first, 20 of 20)

- [Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Space](https://mlsanity.com/paper/2310.02970/) (2023)
- [NP-Match: When Neural Processes meet Semi-Supervised Learning](https://mlsanity.com/paper/2207.01066/) (2022)
- [Deep Learning for Bayesian Optimization of Scientific Problems with High-Dimensional Structure](https://mlsanity.com/paper/2104.11667/) (2021)
- [Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets](https://mlsanity.com/paper/2110.12752/) (2021)
- [PolyNet: Polynomial Neural Network for 3D Shape Recognition with PolyShape Representation](https://mlsanity.com/paper/2110.07882/) (2021)
- [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 in Computer Vision -- Architectures, Datasets and Common Approaches](https://mlsanity.com/paper/2212.10207/) (2022)
- [Regularized Multi-output Gaussian Convolution Process with Domain Adaptation](https://mlsanity.com/paper/2409.02778/) (2024)
- [AdS-GNN -- a Conformally Equivariant Graph Neural Network](https://mlsanity.com/paper/2505.12880/) (2025)
- [Evolving-Graph Gaussian Processes](https://mlsanity.com/paper/2106.15127/) (2021)
- [Geometry-Aware Hierarchical Bayesian Learning on Manifolds](https://mlsanity.com/paper/2111.00184/) (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)
- [Gaussian process deconvolution](https://mlsanity.com/paper/2305.04871/) (2023)
- [When narrower is better: the narrow width limit of Bayesian parallel branching neural networks](https://mlsanity.com/paper/2407.18807/) (2024)
- [Conformalized Gaussian processes for online uncertainty quantification over graphs](https://mlsanity.com/paper/2510.06181/) (2025)
- [Flexible Infinite-Width Graph Convolutional Neural Networks](https://mlsanity.com/paper/2402.06525/) (2024)
- [Multiple-Source Localization from a Single-Snapshot Observation Using Graph Bayesian Optimization](https://mlsanity.com/paper/2403.16818/) (2024)
- [Exploring Probabilistic Models for Semi-supervised Learning](https://mlsanity.com/paper/2404.04199/) (2024)

## Abstract (arXiv)

We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input observations are functions with domains on general graphs. The structure of these models allows for high dimensional inputs while retaining expressibility, as is the case with convolutional neural networks. We present applications of graph convolutional Gaussian processes to images and triangular meshes, demonstrating their versatility and effectiveness, comparing favorably to existing methods, despite being relatively simple models.