Neural Spatio-Temporal Point Processes

TL;DR

This paper introduces a novel neural framework for modeling spatio-temporal point processes using Neural ODEs, continuous-time neural networks, and new architectures, enabling flexible and high-fidelity event modeling across various domains.

Contribution

It presents a new parameterization combining Neural ODEs with Jump and Attentive Continuous-time Normalizing Flows for complex spatio-temporal modeling.

Findings

Effective modeling of diverse spatio-temporal data sets

High-fidelity event distribution learning

Flexible conditioning on event history

Abstract

We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and space. Central to our approach is a combination of continuous-time neural networks with two novel neural architectures, i.e., Jump and Attentive Continuous-time Normalizing Flows. This approach allows us to learn complex distributions for both the spatial and temporal domain and to condition non-trivially on the observed event history. We validate our models on data sets from a wide variety of contexts such as seismology, epidemiology, urban mobility, and neuroscience.