Graph and Simplicial Complex Prediction Gaussian Process via the Hodgelet Representations
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Abstract (arXiv)
Predicting the labels of graph-structured data is crucial in scientific applications and is often achieved using graph neural networks (GNNs). However, when data is scarce, GNNs suffer from overfitting, leading to poor performance. Recently, Gaussian processes (GPs) with graph-level inputs have been proposed as an alternative. In this work, we extend the Gaussian process framework to simplicial complexes (SCs), enabling the handling of edge-level attributes and attributes supported on higher-order simplices. We further augment the resulting SC representations by considering their Hodge decompositions, allowing us to account for homological information, such as the number of holes, in the SC. We demonstrate that our framework enhances the predictions across various applications, paving the way for GPs to be more widely used for graph and SC-level predictions.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 34 of its 41 references that are in the map. First posted on arXiv 16 May 2025.
Builds on
34 of 41 references.
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22 more
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