# Multi-Output Gaussian Processes for Graph-Structured Data

arXiv: https://arxiv.org/abs/2505.16755 · HTML: https://mlsanity.com/paper/2505.16755/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 22 May 2025.

## Builds on (most cited first, 14 of 14)

- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Deep Convolutional Networks on Graph-Structured Data](https://mlsanity.com/paper/1506.05163/) (2015)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Gaussian Processes for Data-Efficient Learning in Robotics and Control](https://mlsanity.com/paper/1502.02860/) (2015)
- [Graph signal processing for machine learning: A review and new perspectives](https://mlsanity.com/paper/2007.16061/) (2020)
- [Mat'ern Gaussian Processes on Graphs](https://mlsanity.com/paper/2010.15538/) (2020)
- [Gaussian Processes on Graphs via Spectral Kernel Learning](https://mlsanity.com/paper/2006.07361/) (2020)
- [A Time-Vertex Signal Processing Framework](https://mlsanity.com/paper/1705.02307/) (2017)
- [Gaussian Processes Over Graphs](https://mlsanity.com/paper/1803.05776/) (2018)
- [Learning parametric dictionaries for graph signals](https://mlsanity.com/paper/1401.0887/) (2014)
- [Gaussian Process Optimization with Mutual Information](https://mlsanity.com/paper/1311.4825/) (2013)
- [DGP-LVM: Derivative Gaussian process latent variable models](https://mlsanity.com/paper/2404.04074/) (2024)
- [Transductive Kernels for Gaussian Processes on Graphs](https://mlsanity.com/paper/2211.15322/) (2022)

## Abstract (arXiv)

Graph-structured data is a type of data to be obtained associated with a graph structure where vertices and edges describe some kind of data correlation. This paper proposes a regression method on graph-structured data, which is based on multi-output Gaussian processes (MOGP), to capture both the correlation between vertices and the correlation between associated data. The proposed formulation is built on the definition of MOGP. This allows it to be applied to a wide range of data configurations and scenarios. Moreover, it has high expressive capability due to its flexibility in kernel design. It includes existing methods of Gaussian processes for graph-structured data as special cases and is possible to remove restrictions on data configurations, model selection, and inference scenarios in the existing methods. The performance of extensions achievable by the proposed formulation is evaluated through computer experiments with synthetic and real data.