Cumulative Hazard Function Based Efficient Multivariate Temporal Point Process Learning

TL;DR

This paper introduces a neural network-based approach to model the cumulative hazard function for multivariate temporal point processes, achieving state-of-the-art performance with fewer parameters and better mathematical properties.

Contribution

It proposes a novel, well-defined CHF modeling method using neural networks, improving scalability and accuracy over existing intensity-based models.

Findings

Achieves state-of-the-art data fitting performance.

Uses significantly fewer parameters and less memory.

Demonstrates effectiveness on six datasets.

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.