  Modeling the dynamics of interacting entities using an evolving graph is an
essential problem in fields such as financial networks and e-commerce.
Traditional approaches focus primarily on pairwise interactions, limiting their
ability to capture the complexity of real-world interactions involving multiple
entities and their intricate relationship structures. This work addresses the
problem of forecasting higher-order interaction events in multi-relational
recursive hypergraphs. This is done using a dynamic graph representation
learning framework that can capture complex relationships involving multiple
entities. The proposed model, \textit{Relational Recursive Hyperedge Temporal
Point Process} (RRHyperTPP) uses an encoder that learns a dynamic node
representation based on the historical interaction patterns and then a
hyperedge link prediction based decoder to model the event's occurrence. These
learned representations are then used for downstream tasks involving
forecasting the type and time of interactions. The main challenge in learning
from hyperedge events is that the number of possible hyperedges grows
exponentially with the number of nodes in the network. This will make the
computation of negative log-likelihood of the temporal point process expensive,
as the calculation of survival function requires a summation over all possible
hyperedges. In our work, we use noise contrastive estimation to learn the
parameters of our model, and we have experimentally shown that our models
perform better than previous state-of-the-art methods for interaction
forecasting.
