A Scalable Inter-edge Correlation Modeling in CopulaGNN for Link Sign Prediction

TL;DR

CopulaLSP addresses link sign prediction on signed graphs by directly modeling inter-edge dependencies with a Gaussian copula. It achieves scalability by representing the inter-edge correlation as a Gramian of edge embeddings and by applying the Woodbury matrix identity to reformulate inference into operations on a small, low-rank matrix, enabling linear convergence and fast training. Empirical results across multiple real-world datasets show competitive predictive performance with substantial speedups in training and inference compared to strong baselines, while ablation confirms the value of the Gramian correlation and the Woodbury reformulation. The work advances scalable, principled inter-edge dependency modeling for signed graphs, with potential applications to dynamic or bipartite graphs in future work.

Abstract

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.

Figures (9)

• Figure 1: CopulaLSP (our proposed model) architecture and its training, inference process.
• Figure 2: Examples of relaxed Bernoulli marginals and a joint PDF using the Gaussian copula
• Figure 3: Convergence of CopulaLSP varying hyperparameter $\eta$.
• Figure 4: Performance of CopulaLSP varying hyperparameter $\eta$.
• Figure I: Embedding size study of CopulaLSP.

Theorems & Definitions (13)

• Theorem 3.1: Woodbury Matrix Identity woodbury_inverting_1950
• Theorem 3.2: Woodbury Reformulation
• proof
• Definition 4.1: Linear Convergence
• Theorem 4.2: Linear Convergence under the Gradient Descent karimi2016linear
• Theorem D.1: Woodbury Reformulation
• proof
• Definition E.1: $L$-smoothness
• Definition E.2: $\mu$-PL Condition polyak1963gradientlojasiewicz1963topological
• Lemma E.3