Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets

Felix Opolka, Yin-Cong Zhi, Pietro Lió, Xiaowen Dong
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:4818-4834, 2022.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-opolka22a, title = { Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets }, author = {Opolka, Felix and Zhi, Yin-Cong and Li\'o, Pietro and Dong, Xiaowen}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {4818--4834}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/opolka22a/opolka22a.pdf}, url = {https://proceedings.mlr.press/v151/opolka22a.html}, abstract = { 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. } }
Endnote
%0 Conference Paper %T Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets %A Felix Opolka %A Yin-Cong Zhi %A Pietro Lió %A Xiaowen Dong %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-opolka22a %I PMLR %P 4818--4834 %U https://proceedings.mlr.press/v151/opolka22a.html %V 151 %X 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.
APA
Opolka, F., Zhi, Y., Lió, P. & Dong, X.. (2022). Adaptive Gaussian Processes on Graphs via Spectral Graph Wavelets . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:4818-4834 Available from https://proceedings.mlr.press/v151/opolka22a.html.

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