Efficient Non-parametric Bayesian Hawkes Processes

In this paper, we develop a non-parametric Bayesian estimation of Hawkes process kernel functions. Our method is based on the cluster representation of Hawkes processes. We sample random branching structures, and thus split the Hawkes process into clusters of Poisson processes, where the intensity function of each of these processes is the nonparametric triggering kernel of the Hawkes process. We derive both a block Gibbs sampler and a maximum a posteriori estimator based on stochastic expectation maximization. On synthetic data, we show our method to be flexible and scalable, and on two largescale Twitter diffusion datasets, we show our method to outperform the parametric Hawkes model. We observe that the learned non-parametric kernel reflects the longevity of different content types. Code has been made publicly available.