Spatio-temporal point processes with deep non-stationary kernels

TL;DR

This paper introduces a novel deep non-stationary influence kernel for spatio-temporal point processes, leveraging low-rank decomposition and neural networks to improve modeling flexibility and computational efficiency.

Contribution

It develops a new deep non-stationary influence kernel with low-rank decomposition, enhancing modeling capacity and efficiency for spatio-temporal point processes.

Findings

Outperforms state-of-the-art methods on simulated data

Demonstrates good computational efficiency

Effectively models non-stationary dependencies

Abstract

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.