将高斯过程扩展到单纯复形，提升稀疏数据下的图与高阶结构预测性能
Graph and Simplicial Complex Prediction Gaussian Process via the Hodgelet Representations
- 基于单纯复形的霍德分解构建图结构表征
- 在低数据场景下优于传统图神经网络
- 适合处理带边属性或高阶关系的科学数据
预测图结构数据的标签在科学应用中至关重要，通常采用图神经网络（GNNs）实现。然而，在数据稀缺时，GNNs 容易过拟合，导致性能下降。近期已有研究提出使用图级别输入的高斯过程（GPs）作为替代方案。本文将高斯过程框架扩展至单纯复形（SCs），可处理边级属性及更高阶单纯形上的属性。我们进一步通过霍德分解增强所得的单纯复形表示，以捕捉同调信息（如洞的数量）。实验表明，该框架在多种应用场景中均提升了预测性能，为高斯过程在图与单纯复形级别的预测中更广泛应用铺平道路。
原文摘要 · Abstract (English)
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.
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