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.

翻译：符号图上的链接符号预测任务旨在判定一条边所代表的关系是正向还是负向。由于负向边的存在违背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此类边时无法直接适用。我们旨在通过高斯Copula及其对应的相关矩阵直接建模边之间的潜在统计依赖关系，从而扩展CopulaGNN（Ma等人，2021）。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，从而显著减少参数量；2）重新形式化条件概率分布，以极大降低推断成本。我们通过证明该方法具有线性收敛性，从理论上验证了其可扩展性。此外，大量实验表明，相较于基线方法，本方法实现了显著更快的收敛速度，同时保持了与最先进模型相竞争的预测性能。