Poisson-Gamma Modeling of Inter-Relational Dependencies in Dynamic Knowledge Graphs

Dynamic knowledge graphs are ubiquitous in today's AI applications, as we represent molecular structures, social relationships, and language information using these graph models. As knowledge graphs evolve over time and are often noisy and incomplete, modeling their temporal and relational dependencies becomes crucial for downstream tasks. To address these challenges, this paper proposes PGRE (Poisson-Gamma Relational Evolution), a probabilistic model for modeling inter-relational dependencies in dynamic knowledge graphs. PGRE represents multi-relational temporal links via a Poisson-Bernoulli formulation. It introduces Gamma-distributed latent variables to capture entity-factor associations and cross-relation dependencies mediated by shared latent communities. A Gamma Markov process further models the temporal evolution of these latent variables, enabling principled characterization of relational dynamics. Experiments on benchmark datasets show that PGRE achieves competitive performance in link prediction, particularly in sparse settings, while revealing meaningful relational evolution patterns in dynamic knowledge graphs.