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. 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.

翻译：符号图上的链接符号预测任务旨在确定一条边所表示的关系是正向还是负向。由于负向边的存在违反了相邻节点相似的图同质性假设，常规图方法在没有辅助结构处理这些负向边时并不适用。我们旨在通过高斯连接函数及其对应的相关矩阵，直接对边之间的潜在统计依赖性进行建模，从而扩展CopulaGNN。然而，即使对于中等规模的图，对边-边关系进行朴素建模在计算上也是不可行的。为解决此问题，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）重新构建条件概率分布，大幅降低推理成本。我们通过证明其线性收敛性，从理论上验证了方法的可扩展性。此外，大量实验表明，该方法比基线模型收敛速度显著更快，同时在预测性能上保持了与最先进模型相当的竞争力。