Dynamic Embeddings of Temporal High-Order Interactions via Neural Diffusion-Reaction Processes

High-order interactions of multiple entities are ubiquitous in practical applications. The associated data often includes the participants, interaction results, and the timestamps when each interaction occurred. While tensor factorization is a popular tool to analyze such data, it often ignores or underuses valuable timestamp information. More important, standard tensor factorization only estimates a static representation for each entity and ignores the temporal variation of the representations. However, such variations might reflect important evolution patterns of the underlying properties of the entities. To address these limitations, we propose Dynamical eMbedIngs of TempoRal hIgh-order interactions (DMITRI). We develop a neural diffusion-reaction process model to estimate the dynamic embeddings for the participant entities. Specifically, based on the observed interactions, we build a multi-partite graph to encode the correlation between the entities. We construct a graph diffusion process to co-evolve the embedding trajectories of the correlated entities and use a neural network to construct a reaction process for each individual entity. In this way, our model is able to capture both the commonalities and personalities during the evolution of the embeddings for different entities. We then use a neural network to model the interaction result as a nonlinear function of the embedding trajectories. For model estimation, we combine ODE solvers to develop a stochastic mini-batch learning algorithm. We propose a simple stratified sampling method to balance the cost of processing each mini-batch so as to improve the overall efficiency. We show the advantage of our approach in both the ablation study and real-world applications.