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Neural Point Process for Learning Spatiotemporal Event Dynamics

Zihao Zhou, Xingyi Yang, Ryan Rossi, Handong Zhao, Rose Yu

TL;DR

The key construction of the approach is the nonparametric space-time intensity function, governed by a latent process, which uses amortized variational inference to infer the latent process with deep networks.

Abstract

Learning the dynamics of spatiotemporal events is a fundamental problem. Neural point processes enhance the expressivity of point process models with deep neural networks. However, most existing methods only consider temporal dynamics without spatial modeling. We propose Deep Spatiotemporal Point Process (\ours{}), a deep dynamics model that integrates spatiotemporal point processes. Our method is flexible, efficient, and can accurately forecast irregularly sampled events over space and time. The key construction of our approach is the nonparametric space-time intensity function, governed by a latent process. The intensity function enjoys closed form integration for the density. The latent process captures the uncertainty of the event sequence. We use amortized variational inference to infer the latent process with deep networks. Using synthetic datasets, we validate our model can accurately learn the true intensity function. On real-world benchmark datasets, our model demonstrates superior performance over state-of-the-art baselines. Our code and data can be found at the https://github.com/Rose-STL-Lab/DeepSTPP.

Neural Point Process for Learning Spatiotemporal Event Dynamics

TL;DR

The key construction of the approach is the nonparametric space-time intensity function, governed by a latent process, which uses amortized variational inference to infer the latent process with deep networks.

Abstract

Learning the dynamics of spatiotemporal events is a fundamental problem. Neural point processes enhance the expressivity of point process models with deep neural networks. However, most existing methods only consider temporal dynamics without spatial modeling. We propose Deep Spatiotemporal Point Process (\ours{}), a deep dynamics model that integrates spatiotemporal point processes. Our method is flexible, efficient, and can accurately forecast irregularly sampled events over space and time. The key construction of our approach is the nonparametric space-time intensity function, governed by a latent process. The intensity function enjoys closed form integration for the density. The latent process captures the uncertainty of the event sequence. We use amortized variational inference to infer the latent process with deep networks. Using synthetic datasets, we validate our model can accurately learn the true intensity function. On real-world benchmark datasets, our model demonstrates superior performance over state-of-the-art baselines. Our code and data can be found at the https://github.com/Rose-STL-Lab/DeepSTPP.
Paper Structure (48 sections, 36 equations, 4 figures, 6 tables, 2 algorithms)

This paper contains 48 sections, 36 equations, 4 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Methodology
  3. Background on Spatiotemporal Point Process
  4. Spatiotemporal Point Process.
  5. Maximum likelihood Estimation.
  6. Predictive distribution.
  7. Deep Spatiotemporal Point Process (DSTPP)
  8. Neural latent process.
  9. Non-parametric model.
  10. Representative Points.
  11. Parameter learning.
  12. Related Work
  13. Spatiotemporal Dynamics Learning.
  14. Continous Time Sequence Models.
  15. Deep Point Process.
  16. ...and 33 more sections

Figures (4)

  • Figure 1: Illustration of learning spatiotemporal point process. We aim to learn the space-time intensity function given the historical event sequence and representative points as background.
  • Figure 2: Design of our DeepSTPP model. For a historical event sequence, we encode it with a transformer network and map to the latent process $(z_1,\cdots, z_n)$. We use a decoder to generate the parameters $(w_i,\gamma_i, \beta_i)$ for each event $i$ given the latent process. The estimate intensity is calculated using kernel functions $k_s$ and $k_t$ and the decoded parameters.
  • Figure 3: Ground-truth and learned intensity on two synthetic data. Top: ground-truth; Middle: learned intensity by our DeepSTPP model. Bottom: learned conditional intensity by NSTPP. The crosses on the top represent the event history, larger crosses are more recent events.
  • Figure 4: Log train time comparison on all datasets