The Hawkes process has been widely applied to modeling self-exciting events, including neuron spikes, earthquakes and tweets. To avoid designing parametric kernel functions and to be able to quantify the prediction confidence, non-parametric Bayesian Hawkes processes have been proposed. However the inference of such models suffers from unscalability or slow convergence. In this paper, we first propose a new non-parametric Bayesian Hawkes process whose triggering kernel is modeled as a squared sparse Gaussian process. Second, we present the variational inference scheme for the model optimization, which has the advantage of linear time complexity by leveraging the stationarity of the triggering kernel. Third, we contribute a tighter lower bound than the evidence lower bound of the marginal likelihood for the model selection. Finally, we exploit synthetic data and large-scale social media data to validate the efficiency of our method and the practical utility of our approximate marginal likelihood. We show that our approach outperforms state-of-the-art non-parametric Bayesian and non-Bayesian methods.

本文提出了一种新的非参数贝叶斯 Hawkes 过程模型，使用稀疏高斯过程来建模触发核，进而通过新颖的变分推断方案，实现了模型优化的效率提升。通过使用不同的数据集进行了对比，结果表明本方法在模型选择及预测准确性方面均优于现有的频率派和贝叶斯方法。

稀疏高斯过程调制霍克斯过程的变分推断