Local low-rank Hawkes processes for modeling temporal user-item interactions

Hawkes processes have become very popular in modeling multiple recurrent user-item interaction events that exhibit mutual-excitation properties in various domains. Generally, modeling the interaction sequence of each user-item pair as an independent Hawkes process is ineffective since the prediction accuracy of future event occurrences for users and items with few observed interactions is low. On the other hand, multivariate Hawkes processes (MHPs) can be used to handle multi-dimensional random processes where different dimensions are correlated with each other. However, an MHP either fails to describe the correct mutual influence between dimensions or become computational inhibitive in most real-world events involving a large collection of users and items. To tackle this challenge, we propose local low-rank Hawkes processes to model large-scale user-item interactions, which efficiently captures the correlations of Hawkes processes in different dimensions. In addition, we design an efficient convex optimization algorithm to estimate model parameters and present a parallel algorithm to further increase the computation efficiency. Extensive experiments on real-world datasets demonstrate the performance improvements of our model in comparison with the state of the art.