ArXiv Preprint
Point process data are becoming ubiquitous in modern applications, such as
social networks, health care, and finance. Despite the powerful expressiveness
of the popular recurrent neural network (RNN) models for point process data,
they may not successfully capture sophisticated non-stationary dependencies in
the data due to their recurrent structures. Another popular type of deep model
for point process data is based on representing the influence kernel (rather
than the intensity function) by neural networks. We take the latter approach
and develop a new deep non-stationary influence kernel that can model
non-stationary spatio-temporal point processes. The main idea is to approximate
the influence kernel with a novel and general low-rank decomposition, enabling
efficient representation through deep neural networks and computational
efficiency and better performance. We also take a new approach to maintain the
non-negativity constraint of the conditional intensity by introducing a
log-barrier penalty. We demonstrate our proposed method's good performance and
computational efficiency compared with the state-of-the-art on simulated and
real data.
Zheng Dong, Xiuyuan Cheng, Yao Xie
2022-11-21
