Tensor decompositions are fundamental tools for multiway data analysis. Existing approaches, however, ignore the valuable temporal information along with data, or simply discretize them into time steps so that important temporal patterns are easily missed. Moreover, most methods are limited to multilinear decomposition forms, and hence are unable to capture intricate, nonlinear relationships in data. To address these issues, we formulate event-tensors, to preserve the complete temporal information for multiway data, and propose a novel Bayesian nonparametric decomposition model. Our model can (1) fully exploit the time stamps to capture the critical, causal/triggering effects between the interaction events, (2) flexibly estimate the complex relationships between the entities in tensor modes, and (3) uncover hidden structures from their temporal interactions. For scalable inference, we develop a doubly stochastic variational Expectation-Maximization algorithm to conduct an online decomposition. Evaluations on both synthetic and real-world datasets show that our model not only improves upon the predictive performance of existing methods, but also discovers interesting clusters underlying the data.

The work proposed a nonparametric Bayesian model for event tensor decomposition. Existing tensor works lack of a way to integrate the complete temporal information in the factorization. This work formulates the so called "event-tensor" to preserver all the time stamps, where each entry consists of a sequence of events rather than a value. To decompose the event-tensor, the work hybridizes Gaussian processes and Hawkes processes to model the entries as mutually excited Hawkes processes, and base rates Gaussian processes on the latent factors. The authors exploit the Poisson process super-position theorem and variational sparse GP framework to derive a decomposable variational lower bound and develop a doubly stochastic algorithm for scalable inference.

Tensor decompositions are fundamental tools for multiway data analysis. Existing approaches, however, ignore the valuable temporal information along with data, or simply discretize them into time steps so that important temporal patterns are easily missed. Moreover, most methods are limited to multilinear decomposition forms, and hence are unable to capture intricate, nonlinear relationships in data. To address these issues, we formulate event-tensors, to preserve the complete temporal information for multiway data, and propose a novel Bayesian nonparametric decomposition model. Our model can (1) fully exploit the time stamps to capture the critical, causal/triggering effects between the interaction events, (2) flexibly estimate the complex relationships between the entities in tensor modes, and (3) uncover hidden structures from their temporal interactions.