Scalable Nonparametric Factorization for High-Order Interaction Events

Interaction events among multiple entities are ubiquitous in real-world applications. Although these interactions can be naturally represented by tensors and analyzed by tensor decomposition, most existing approaches are limited to multilinear decomposition forms, and cannot estimate complex, nonlinear relationships in data. More importantly, the existing approaches severely underexploit the time stamps information. They either drop/discretize the time stamps or set a local window to ignore the long-term dependency between the events. To address these issues, we propose a Bayesian nonparametric factorization model for high-order interaction events, which can flexibly estimate/embed the static, nonlinear relationships and capture various long-term and short-term excitations effects, encoding these effects and their decaying patterns into the latent factors. Specifically, we use the latent factors to construct a set of mutually excited Hawkes processes, where we place a Gaussian process prior over the background rates to estimate the static, nonlinear relationships of the entities and propose novel triggering kernels to embed the excitation strengths and their time decaying rates among the interactions. For scalable inference, we derive a fully-decomposed model evidence lower bound to dispose of the huge covariance matrix and expensive log summation terms. Then we develop an efficient stochastic optimization algorithm. We show the advantage of our approach in four real-world applications.