Adaptive Gaussian processes on graphs via spectral graph wavelets

Conference item

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.

Authors: Opolka, FL; Zhi, YC; Liò, P; Dong, X

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Proceedings of Machine Learning Research
• Host title: Proceedings of the 25th International Conference on Artificial Intelligence and Statistics
• Pages: 4818-4834
• Series: Proceedings of Machine Learning Research
• Series number: 151
• Publication date: 2022-05-03
• Event title: 25th International Conference on Artificial Intelligence and Statistics (AISTATS 2022)
• Event location: Virtual event
• Event website: http://aistats.org/aistats2022/
• Event start date: 2022-03-28
• Event end date: 2022-03-30
• EISSN: 2640-3498
• Language: English