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Cumulative Hazard Function Based Efficient Multivariate Temporal Point Process Learning

Bingqing Liu

TL;DR

The paper addresses scalable, accurate modeling of multivariate temporal point processes by directly learning a well-defined cumulative hazard function (CHF) and a time-dependent type distribution, enabling exact likelihood evaluation with far fewer parameters than traditional intensity-based methods. It introduces a CHF network with monotonicity constraints and a history-dependent residual to capture base intensity, along with a lightweight time predictor and a time-dependent type predictor to model event types conditioned on inter-event times. Across six datasets, the approach achieves state-of-the-art data fitting and event prediction while significantly reducing memory usage and parameter counts, outperforming both intensity-based and prior CHF-based methods. The work demonstrates the practical impact of CHF-based learning for scalable, accurate point process modeling in real-world, multi-type event data.

Abstract

Most existing temporal point process models are characterized by conditional intensity function. These models often require numerical approximation methods for likelihood evaluation, which potentially hurts their performance. By directly modelling the integral of the intensity function, i.e., the cumulative hazard function (CHF), the likelihood can be evaluated accurately, making it a promising approach. However, existing CHF-based methods are not well-defined, i.e., the mathematical constraints of CHF are not completely satisfied, leading to untrustworthy results. For multivariate temporal point process, most existing methods model intensity (or density, etc.) functions for each variate, limiting the scalability. In this paper, we explore using neural networks to model a flexible but well-defined CHF and learning the multivariate temporal point process with low parameter complexity. Experimental results on six datasets show that the proposed model achieves the state-of-the-art performance on data fitting and event prediction tasks while having significantly fewer parameters and memory usage than the strong competitors. The source code and data can be obtained from https://github.com/lbq8942/NPP.

Cumulative Hazard Function Based Efficient Multivariate Temporal Point Process Learning

TL;DR

The paper addresses scalable, accurate modeling of multivariate temporal point processes by directly learning a well-defined cumulative hazard function (CHF) and a time-dependent type distribution, enabling exact likelihood evaluation with far fewer parameters than traditional intensity-based methods. It introduces a CHF network with monotonicity constraints and a history-dependent residual to capture base intensity, along with a lightweight time predictor and a time-dependent type predictor to model event types conditioned on inter-event times. Across six datasets, the approach achieves state-of-the-art data fitting and event prediction while significantly reducing memory usage and parameter counts, outperforming both intensity-based and prior CHF-based methods. The work demonstrates the practical impact of CHF-based learning for scalable, accurate point process modeling in real-world, multi-type event data.

Abstract

Most existing temporal point process models are characterized by conditional intensity function. These models often require numerical approximation methods for likelihood evaluation, which potentially hurts their performance. By directly modelling the integral of the intensity function, i.e., the cumulative hazard function (CHF), the likelihood can be evaluated accurately, making it a promising approach. However, existing CHF-based methods are not well-defined, i.e., the mathematical constraints of CHF are not completely satisfied, leading to untrustworthy results. For multivariate temporal point process, most existing methods model intensity (or density, etc.) functions for each variate, limiting the scalability. In this paper, we explore using neural networks to model a flexible but well-defined CHF and learning the multivariate temporal point process with low parameter complexity. Experimental results on six datasets show that the proposed model achieves the state-of-the-art performance on data fitting and event prediction tasks while having significantly fewer parameters and memory usage than the strong competitors. The source code and data can be obtained from https://github.com/lbq8942/NPP.
Paper Structure (17 sections, 14 equations, 4 figures, 6 tables)

This paper contains 17 sections, 14 equations, 4 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Preliminaries and Related Work
  3. Temporal Point Process
  4. Neural Point Process
  5. Method
  6. Multivariate Temporal Point Process
  7. Model Architecture
  8. Training Loss
  9. Experiment
  10. Datasets
  11. Baselines
  12. Implementation Details
  13. Data Fitting
  14. Event prediction
  15. Model Complexity
  16. ...and 2 more sections

Figures (4)

  • Figure 1: The proposed cumulative hazard function (CHF) based multivariate temporal point process model, including three modules: the CHF network, the time predictor and the time-dependent type predictor. The CHF network is to reproduce a well-defined CHF so as to capture the temporal dynamics, the time predictor is for time prediction, and the time-dependent type predictor is to capture the dynamics of event types and also used for type prediction.
  • Figure 2: Case study: two learned probability density functions on dataset SOflow. The proposed model and JTPP fit the ground truth time more exactly.
  • Figure 3: The fitting performance and required parameters for baselines and the proposed model on datasets Hawkes1, SOflow, MIMIC and Social. In each plot, models locate in the bottom and left are better.
  • Figure 4: Training curves of the proposed model using different activation functions for the cumulative hazard function network, fitted on dataset Retweet.