Summation overi I decouples i from j and allows reuse of computation overj.

Higher-order interactions (HOIs) in complex systems, such as scientific collaborations, multi-protein complexes, and multi-user communications, are commonly modeled as hypergraphs, where each hyperedge (i.e., a subset of nodes) represents an HOI among the nodes. Given a hypergraph, hyperedge prediction aims to identify hyperedges that are either missing or likely to form in the future, and it has broad applications, including recommending interest-based social groups, predicting collaborations, and uncovering functional complexes in biological systems. However, the vast search space of hyperedge candidates (i.e., all possible subsets of nodes) poses a significant computational challenge, making naive exhaustive search infeasible. As a result, existing approaches rely on either heuristic sampling to obtain constrained candidate sets or ungrounded assumptions on hypergraph structure to select promising hyperedges. In this work, we propose HyperSearch, a search-based algorithm for hyperedge prediction that efficiently evaluates unconstrained candidate sets, by incorporating two key components: (1) an empirically grounded scoring function derived from observations in real-world hypergraphs and (2) an efficient search mechanism, where we derive and use an anti-monotonic upper bound of the original scoring function (which is not antimonotonic) to prune the search space. This pruning comes with theoretical guarantees, ensuring that discarded candidates are never better than the kept ones w.r.t. the original scoring function. In extensive experiments on 10 real-world hypergraphs across five domains, HyperSearch consistently outperforms state-of-the-art baselines, achieving higher accuracy in predicting new (i.e., not in the training set) hyperedges.

Deep graph models have achieved great success in network representation learning. However, their focus on pairwise relationships restricts their ability to learn pervasive higher-order interactions in real-world systems, which can be naturally modeled as hypergraphs. To tackle this issue, Hypergraph Neural Networks (HNNs) have garnered substantial attention in recent years. Despite the proposal of numerous HNNs, the absence of consistent experimental protocols and multi-dimensional empirical analysis impedes deeper understanding and further development of HNN research. While several toolkits for deep hypergraph learning (DHGL) have been introduced to facilitate algorithm evaluation, they provide only limited quantitative evaluation results and insufficient coverage of advanced algorithms, datasets, and benchmark tasks. To fill the gap, we introduce DHG-Bench, the first comprehensive benchmark for HNNs. Specifically, DHG-Bench systematically investigates the characteristics of HNNs in terms of four dimensions: effectiveness, efficiency, robustness, and fairness. We comprehensively evaluate 17 state-of-the-art HNN algorithms on 22 diverse datasets spanning node-, edge-, and graph-level tasks, under unified experimental settings. Extensive experiments reveal both the strengths and limitations of existing algorithms, offering valuable insights and directions for future research. Furthermore, to facilitate reproducible research, we have developed an easy-to-use library for training and evaluating different HNN methods. The DHG-Bench library is available at: https://github.com/Coco-Hut/DHG-Bench.

Groups with complex set intersection relations are a natural way to model a wide array of data, from the formation of social groups to the complex protein interactions which form the basis of biological life. One approach to representing such "higher order" relationships is as a hypergraph. However, efforts to apply machine learning techniques to hypergraph structured datasets have been limited thus far. In this paper, we address the problem of link prediction in knowledge hypergraphs as well as simple hypergraphs and develop a novel, simple, and effective optimization architecture that addresses both tasks. Additionally, we introduce a novel feature extraction technique using node level clustering and we show how integrating data from node-level labels can improve system performance. Our self-supervised approach achieves significant improvement over state of the art baselines on several hyperedge prediction and knowledge hypergraph completion benchmarks.

Hypergraphs can naturally model group-wise relations (e.g., a group of users who co-purchase an item) as hyperedges. Hyperedge prediction is to predict future or unobserved hyperedges, which is a fundamental task in many real-world applications (e.g., group recommendation). Despite the recent breakthrough of hyperedge prediction methods, the following challenges have been rarely studied: (C1) How to aggregate the nodes in each hyperedge candidate for accurate hyperedge prediction? and (C2) How to mitigate the inherent data sparsity problem in hyperedge prediction? To tackle both challenges together, in this paper, we propose a novel hyperedge prediction framework (CASH) that employs (1) context-aware node aggregation to precisely capture complex relations among nodes in each hyperedge for (C1) and (2) self-supervised contrastive learning in the context of hyperedge prediction to enhance hypergraph representations for (C2). Furthermore, as for (C2), we propose a hyperedge-aware augmentation method to fully exploit the latent semantics behind the original hypergraph and consider both node-level and group-level contrasts (i.e., dual contrasts) for better node and hyperedge representations. Extensive experiments on six real-world hypergraphs reveal that CASH consistently outperforms all competing methods in terms of the accuracy in hyperedge prediction and each of the proposed strategies is effective in improving the model accuracy of CASH. For the detailed information of CASH, we provide the code and datasets at: https://github.com/yy-ko/cash.