用高斯核建模边间相关性，让签名图链接预测更快更准。
A Scalable Inter-edge Correlation Modeling in CopulaGNN for Link Sign Prediction
- 用边嵌入的格拉姆矩阵表示边相关性，大幅降低参数量
- 新概率公式使推理成本显著下降，支持中等规模图
- 理论证明线性收敛，实测比基线快且精度不输顶尖模型
在符号图上进行链接符号预测，旨在判断边所代表的关系是正向还是负向。由于负边违反了邻近节点相似的图同质性假设，传统图方法需依赖辅助结构才能适用。本文直接通过高斯耦合及其相关矩阵建模边间的潜在统计依赖关系，扩展了CopulaGNN（Ma et al., 2021）。然而，直接建模边间关系在中等规模图上仍计算不可行。为此，我们提出：1）将相关矩阵表示为边嵌入的格拉姆矩阵，显著减少参数数量；2）重构条件概率分布，大幅降低推理开销。理论上证明了方法的可扩展性，证明其具有线性收敛性。大量实验表明，该方法在保持与最先进模型相当预测性能的同时，收敛速度显著优于基线。
原文摘要 · Abstract (English)
Link sign prediction on a signed graph is a task to determine whether the relationship represented by an edge is positive or negative. Since the presence of negative edges violates the graph homophily assumption that adjacent nodes are similar, regular graph methods have not been applicable without auxiliary structures to handle them. We aim to directly model the latent statistical dependency among edges with the Gaussian copula and its corresponding correlation matrix, extending CopulaGNN (Ma et al., 2021). However, a naive modeling of edge-edge relations is computationally intractable even for a graph with moderate scale. To address this, we propose to 1) represent the correlation matrix as a Gramian of edge embeddings, significantly reducing the number of parameters, and 2) reformulate the conditional probability distribution to dramatically reduce the inference cost. We theoretically verify scalability of our method by proving its linear convergence. Also, our extensive experiments demonstrate that it achieves significantly faster convergence than baselines, maintaining competitive prediction performance to the state-of-the-art models.
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