Gaussian Processes on Cellular Complexes

Mathieu Alain, So Takao, Brooks Paige, Marc Peter Deisenroth
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:879-905, 2024.

Abstract

In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gaussian processes on such structures since they can additionally account for uncertainty. However, graphs are limited to modelling relations between two vertices. In this paper, we go beyond this dyadic setting and consider polyadic relations that include interactions between vertices, edges and one of their generalisations, known as cells. Specifically, we propose Gaussian processes on cellular complexes, a generalisation of graphs that captures interactions between these higher-order cells. One of our key contributions is the derivation of two novel kernels, one that generalises the graph Matérn kernel and one that additionally mixes information of different cell types.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-alain24a, title = {{G}aussian Processes on Cellular Complexes}, author = {Alain, Mathieu and Takao, So and Paige, Brooks and Deisenroth, Marc Peter}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {879--905}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/alain24a/alain24a.pdf}, url = {https://proceedings.mlr.press/v235/alain24a.html}, abstract = {In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gaussian processes on such structures since they can additionally account for uncertainty. However, graphs are limited to modelling relations between two vertices. In this paper, we go beyond this dyadic setting and consider polyadic relations that include interactions between vertices, edges and one of their generalisations, known as cells. Specifically, we propose Gaussian processes on cellular complexes, a generalisation of graphs that captures interactions between these higher-order cells. One of our key contributions is the derivation of two novel kernels, one that generalises the graph Matérn kernel and one that additionally mixes information of different cell types.} }
Endnote
%0 Conference Paper %T Gaussian Processes on Cellular Complexes %A Mathieu Alain %A So Takao %A Brooks Paige %A Marc Peter Deisenroth %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-alain24a %I PMLR %P 879--905 %U https://proceedings.mlr.press/v235/alain24a.html %V 235 %X In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gaussian processes on such structures since they can additionally account for uncertainty. However, graphs are limited to modelling relations between two vertices. In this paper, we go beyond this dyadic setting and consider polyadic relations that include interactions between vertices, edges and one of their generalisations, known as cells. Specifically, we propose Gaussian processes on cellular complexes, a generalisation of graphs that captures interactions between these higher-order cells. One of our key contributions is the derivation of two novel kernels, one that generalises the graph Matérn kernel and one that additionally mixes information of different cell types.
APA
Alain, M., Takao, S., Paige, B. & Deisenroth, M.P.. (2024). Gaussian Processes on Cellular Complexes. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:879-905 Available from https://proceedings.mlr.press/v235/alain24a.html.

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