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arXiv 2602.17115stat.MLcs.LG
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基于图神经网络的图半监督学习

Semi-Supervised Learning on Graphs using Graph Neural Networks

School of Mathematical Sciences, Xiamen University(厦门大学数学科学学院);Department of Statistics, University of Chicago(芝加哥大学统计系);ESSEC Business School(ESSEC商学院);Department of Applied Mathematics, University of Twente(特文特大学应用数学系)

Juntong Chen, Claire Donnat, Olga Klopp, Johannes Schmidt-Hieber

AI总结:

本文提出了一种基于图神经网络的聚合-读出模型,通过理论分析和实验验证,揭示了GNN在半监督学习中性能与标签比例及图依赖性的关系。

摘要:

图神经网络(GNNs)在半监督节点回归任务中表现非常出色,但缺乏能够解释何时以及为何成功的严谨理论。为填补这一空白,我们研究了一种聚合-读出模型,该模型涵盖了几种常见的消息传递架构:节点特征首先在图上传播,然后通过非线性函数映射到响应。对于使用线性图卷积和深度ReLU读出的GNN的最小二乘估计,我们证明了一个尖锐的非渐近风险界,该界区分了逼近、随机和优化误差。该界明确说明了性能如何随标记节点的比例和图诱导依赖性变化。进一步推导了图平滑后接光滑非线性读出的逼近保证,得出的收敛率在完全监督下恢复了经典非参数行为,同时在标签稀缺时刻画了性能。数值实验验证了我们的理论,提供了一个系统框架来理解GNN的性能和限制。

英文摘要:

Graph neural networks (GNNs) work remarkably well in semi-supervised node regression, yet a rigorous theory explaining when and why they succeed remains lacking. To address this gap, we study an aggregate-and-readout model that encompasses several common message passing architectures: node features are first propagated over the graph then mapped to responses via a nonlinear function. For least-squares estimation over GNNs with linear graph convolutions and a deep ReLU readout, we prove a sharp non-asymptotic risk bound that separates approximation, stochastic, and optimization errors. The bound makes explicit how performance scales with the fraction of labeled nodes and graph-induced dependence. Approximation guarantees are further derived for graph-smoothing followed by smooth nonlinear readouts, yielding convergence rates that recover classical nonparametric behavior under full supervision while characterizing performance when labels are scarce. Numerical experiments validate our theory, providing a systematic framework for understanding GNN performance and limitations.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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