Neural Jump-Diffusion Temporal Point Processes
Shuai Zhang, Chuan Zhou, Yang Aron Liu, Peng Zhang, Xixun Lin, Zhi-Ming Ma
Abstract
We present a novel perspective on temporal point processes (TPPs) by reformulating their intensity processes as solutions to stochastic differential equations (SDEs). In particular, we first prove the equivalent SDE formulations of several classical TPPs, including Poisson processes, Hawkes processes, and self-correcting processes. Based on these proofs, we introduce a unified TPP framework called Neural Jump-Diffusion Temporal Point Process (NJDTPP), whose intensity process is governed by a neural jump-diffusion SDE (NJDSDE) where the drift, diffusion, and jump coefficient functions are parameterized by neural networks. Compared to previous works, NJDTPP exhibits model flexibility in capturing intensity dynamics without relying on any specific functional form, and provides theoretical guarantees regarding the existence and uniqueness of the solution to the proposed NJDSDE. Experiments on both synthetic and real-world datasets demonstrate that NJDTPP is capable of capturing the dynamics of intensity processes in different scenarios and significantly outperforms the state-of-the-art TPP models in prediction tasks.
BibTeX
@inproceedings{
zhang2024neural,
title={Neural Jump-Diffusion Temporal Point Processes},
author={Shuai Zhang and Chuan Zhou and Yang Aron Liu and Peng Zhang and Xixun Lin and Zhi-Ming Ma},
booktitle={Forty-first International Conference on Machine Learning},
year={2024},
url={https://openreview.net/forum?id=d1P6GtRzuV}
}