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

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.

Graph Spectral Filtering with Chebyshev Interpolation for Recommendation

Graph convolutional networks have recently gained prominence in collaborative filtering (CF) for recommendations. However, we identify potential bottlenecks in two foundational components. First, the embedding layer leads to a latent space with limited capacity, overlooking locally observed but potentially valuable preference patterns. Also, the widely-used neighborhood aggregation is limited in its ability to leverage diverse preference patterns in a fine-grained manner. Building on spectral graph theory, we reveal that these limitations stem from graph filtering with a cut-off in the frequency spectrum and a restricted linear form. To address these issues, we introduce ChebyCF, a CF framework based on graph spectral filtering. Instead of a learned embedding, it takes a user's raw interaction history to utilize the full spectrum of signals contained in it. Also, it adopts Chebyshev interpolation to effectively approximate a flexible non-linear graph filter, and further enhances it by using an additional ideal pass filter and degree-based normalization. Through extensive experiments, we verify that ChebyCF overcomes the aforementioned bottlenecks and achieves state-of-the-art performance across multiple benchmarks and reasonably fast inference. Our code is available at https://github.com/chanwoo0806/ChebyCF.