# Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets

arXiv: https://arxiv.org/abs/2110.12752 · HTML: https://mlsanity.com/paper/2110.12752/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 52 references that are in the map.
- First posted on arXiv 25 Oct 2021.

## Builds on (most cited first, 27 of 27)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Beyond Low-frequency Information in Graph Convolutional Networks](https://mlsanity.com/paper/2101.00797/) (2021)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [LanczosNet: Multi-Scale Deep Graph Convolutional Networks](https://mlsanity.com/paper/1901.01484/) (2019)
- [Mat'ern Gaussian Processes on Graphs](https://mlsanity.com/paper/2010.15538/) (2020)
- [Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networks](https://mlsanity.com/paper/2003.08414/) (2020)
- [Geometric Scattering for Graph Data Analysis](https://mlsanity.com/paper/1810.03068/) (2018)
- [How Framelets Enhance Graph Neural Networks](https://mlsanity.com/paper/2102.06986/) (2021)
- [Diffusion Scattering Transforms on Graphs](https://mlsanity.com/paper/1806.08829/) (2018)
- [Bayesian Semi-supervised Learning with Graph Gaussian Processes](https://mlsanity.com/paper/1809.04379/) (2018)
- [Gaussian Processes on Graphs via Spectral Kernel Learning](https://mlsanity.com/paper/2006.07361/) (2020)
- [Graph Convolutional Gaussian Processes](https://mlsanity.com/paper/1905.05739/) (2019)
- [Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames](https://mlsanity.com/paper/1311.0897/) (2013)
- [Gaussian Processes Over Graphs](https://mlsanity.com/paper/1803.05776/) (2018)
- [Graph Convolutional Gaussian Processes For Link Prediction](https://mlsanity.com/paper/2002.04337/) (2020)
- [Stacked Graph Filter](https://mlsanity.com/paper/2011.10988/) (2020)
- [Structured sampling and fast reconstruction of smooth graph signals](https://mlsanity.com/paper/1705.02202/) (2017)
- [Dynamic Embedding on Textual Networks via a Gaussian Process](https://mlsanity.com/paper/1910.02187/) (2019)

## Built on by (most cited first, 11 of 11)

- [Gaussian Processes on Cellular Complexes](https://mlsanity.com/paper/2311.01198/) (2023)
- [Bayesian Optimisation of Functions on Graphs](https://mlsanity.com/paper/2306.05304/) (2023)
- [Graph Classification Gaussian Processes via Spectral Features](https://mlsanity.com/paper/2306.03770/) (2023)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [A General Graph Spectral Wavelet Convolution via Chebyshev Order Decomposition](https://mlsanity.com/paper/2405.13806/) (2024)
- [Transductive Kernels for Gaussian Processes on Graphs](https://mlsanity.com/paper/2211.15322/) (2022)
- [Ksurf-Drone: Attention Kalman Filter for Contextual Bandit Optimization in Cloud Resource Allocation](https://mlsanity.com/paper/2511.09766/) (2025)
- [Graph Spectral Embedding using the Geodesic Betweeness Centrality](https://mlsanity.com/paper/2205.03544/) (2022)
- [Multiple-Source Localization from a Single-Snapshot Observation Using Graph Bayesian Optimization](https://mlsanity.com/paper/2403.16818/) (2024)
- [Data-Driven Graph Filters via Adaptive Spectral Shaping](https://mlsanity.com/paper/2602.03698/) (2026)
- [Can Graph Foundation Models Generalize Over Architecture?](https://mlsanity.com/paper/2603.22984/) (2026)

## Abstract (arXiv)

Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the relevant information. In this work, we propose a Gaussian process model using spectral graph wavelets, which can naturally aggregate neighbourhood information at different scales. Through maximum likelihood optimisation of the model hyperparameters, the wavelets automatically adapt to the different frequencies in the data, and as a result our model goes beyond capturing low frequency information. We achieve scalability to larger graphs by using a spectrum-adaptive polynomial approximation of the filter function, which is designed to yield a low approximation error in dense areas of the graph spectrum. Synthetic and real-world experiments demonstrate the ability of our model to infer scales accurately and produce competitive performances against state-of-the-art models in graph-based learning tasks.