Spatio-temporal point processes with deep non-stationary kernels
This work addresses the challenge of capturing sophisticated non-stationary patterns in point process data for applications like social networks, health care, and finance, representing an incremental advancement over existing deep learning approaches.
The authors tackled the problem of modeling non-stationary dependencies in spatio-temporal point process data, which existing RNN-based methods may not capture effectively, by developing a new deep non-stationary influence kernel with a low-rank decomposition and a log-barrier penalty for non-negativity constraints, resulting in improved performance and computational efficiency compared to state-of-the-art methods on simulated and real data.
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.