Hodge-Compositional Edge Gaussian Processes

Maosheng Yang, Viacheslav Borovitskiy, Elvin Isufi
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:3754-3762, 2024.

Abstract

We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning flow-type data on networks where edge flows can be characterized by the discrete divergence and curl. Drawing upon the Hodge decomposition, we first develop classes of divergence-free and curl-free edge GPs, suitable for various applications. We then combine them to create Hodge-compositional edge GPs that are expressive enough to represent any edge function. These GPs facilitate direct and independent learning for the different Hodge components of edge functions, enabling us to capture their relevance during hyperparameter optimization. To highlight their practical potential, we apply them for flow data inference in currency exchange, ocean currents and water supply networks, comparing them to alternative models.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-yang24e, title = { Hodge-Compositional Edge {G}aussian Processes }, author = {Yang, Maosheng and Borovitskiy, Viacheslav and Isufi, Elvin}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {3754--3762}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/yang24e/yang24e.pdf}, url = {https://proceedings.mlr.press/v238/yang24e.html}, abstract = { We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning flow-type data on networks where edge flows can be characterized by the discrete divergence and curl. Drawing upon the Hodge decomposition, we first develop classes of divergence-free and curl-free edge GPs, suitable for various applications. We then combine them to create Hodge-compositional edge GPs that are expressive enough to represent any edge function. These GPs facilitate direct and independent learning for the different Hodge components of edge functions, enabling us to capture their relevance during hyperparameter optimization. To highlight their practical potential, we apply them for flow data inference in currency exchange, ocean currents and water supply networks, comparing them to alternative models. } }
Endnote
%0 Conference Paper %T Hodge-Compositional Edge Gaussian Processes %A Maosheng Yang %A Viacheslav Borovitskiy %A Elvin Isufi %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-yang24e %I PMLR %P 3754--3762 %U https://proceedings.mlr.press/v238/yang24e.html %V 238 %X We propose principled Gaussian processes (GPs) for modeling functions defined over the edge set of a simplicial 2-complex, a structure similar to a graph in which edges may form triangular faces. This approach is intended for learning flow-type data on networks where edge flows can be characterized by the discrete divergence and curl. Drawing upon the Hodge decomposition, we first develop classes of divergence-free and curl-free edge GPs, suitable for various applications. We then combine them to create Hodge-compositional edge GPs that are expressive enough to represent any edge function. These GPs facilitate direct and independent learning for the different Hodge components of edge functions, enabling us to capture their relevance during hyperparameter optimization. To highlight their practical potential, we apply them for flow data inference in currency exchange, ocean currents and water supply networks, comparing them to alternative models.
APA
Yang, M., Borovitskiy, V. & Isufi, E.. (2024). Hodge-Compositional Edge Gaussian Processes . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:3754-3762 Available from https://proceedings.mlr.press/v238/yang24e.html.

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