Subgraph neural networks have recently gained prominence for various subgraph-level predictive tasks. However, existing methods either \emph{1)} apply simple standard pooling over graph convolutional networks, failing to capture essential subgraph properties, or \emph{2)} rely on rigid subgraph definitions, leading to suboptimal performance. Moreover, these approaches fail to model long-range dependencies both between and within subgraphs—a critical limitation, as many real-world networks contain subgraphs of varying sizes and connectivity patterns. In this paper, we propose a novel implicit subgraph neural network, the first of its kind, designed to capture dependencies across subgraphs. Our approach also integrates label-aware subgraph-level information. We formulate implicit subgraph learning as a bilevel optimization problem and develop a provably convergent algorithm that requires fewer gradient estimations than standard bilevel optimization methods. We evaluate our approach on real-world networks against state-of-the-art baselines, demonstrating its effectiveness and superiority.

Accurate health risk prediction is crucial for making informed clinical decisions and assessing the appropriate allocation of medical resources. While recent deep learning based approaches have shown great promise in risk prediction, they primarily focus on modeling the sequential information in Electronic Health Records (EHRs) and fail to leverage the rich mobility interactions among health entities. As a result, the existing approaches yield unsatisfactory performance in downstream risk prediction tasks, especially tasks such as Clostridioides difficile Infection (CDI) incidence prediction that are primarily spread through mobility interactions. To address this issue, we propose a new approach that leverages Hypergraphs to explicitly model mobility interactions to improve predictive performance in health risk prediction tasks. Unlike regular graphs that are limited to modeling pairwise relationships, hypergraphs can effectively characterize the complex high-order semantic relationships between patients. Moreover, we introduce a new contrastive learning strategy that exploits the domain knowledge to generate semantically meaningful positive (homologous) and negative (heterologous) pairs needed for contrastive learning. This unique contrastive pair augmentation strategy boosts the power of contrastive learning by generating feature representations that are both robust and well-aligned with the domain knowledge. Experiments on two real-world datasets demonstrate the advantage of our approach in both short-term and long-term risk prediction tasks, such as CDI incidence prediction and MICU transfer prediction. Our framework obtains gains in performance up to 29.49 % for PHOP, 30.64 % for MIMIC-IV for MICU transfer prediction, 13.17 % for PHOP, and 4.45 % for MIMIC-IV for CDI Incidence Prediction.

Implicit graph neural networks have gained popularity in recent years as they capture long-range dependencies while improving predictive performance in static graphs. Despite the tussle between performance degradation due to the oversmoothing of learned embeddings and long-range dependency being more pronounced in dynamic graphs, as features are aggregated both across neighborhood and time, no prior work has proposed an implicit graph neural model in a dynamic setting.