Bayesian Nonparametric Hawkes Processes

Published in Bayesian Nonparametrics Workshop at NeurIPS18, 2018

Bayesian nonparametric priors (BNPs) have risen in popularity to capture the latent structure behind streams of data whose temporal nature has been modeled with Hawkes processes (HPs). However, a closer look into the literature reveals that many of these works do not actually rely on a valid BNP model. This is due to the fact that their BNP construction leads to patterns that “vanish” over time, i.e., that are assigned zero probability. In this work, we formalize this problem and develop a general and modular methodology to avoid the vanishing prior issue while, at the same time, allowing us to place a valid BNP over event data of an HP. The proposed methodology is general enough to model users’ activity and interactions, as well as to incorporate any valid BNP prior (e.g., the Chinese Restaurant Process and its hierarchical and nested variants).