Neural Jump-Diffusion Temporal Point Processes

Shuai Zhang, Chuan Zhou, Yang Aron Liu, Peng Zhang, Xixun Lin, Zhi-Ming Ma
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:60541-60557, 2024.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-zhang24cm, title = {Neural Jump-Diffusion Temporal Point Processes}, author = {Zhang, Shuai and Zhou, Chuan and Liu, Yang Aron and Zhang, Peng and Lin, Xixun and Ma, Zhi-Ming}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {60541--60557}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/zhang24cm/zhang24cm.pdf}, url = {https://proceedings.mlr.press/v235/zhang24cm.html}, 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.} }
Endnote
%0 Conference Paper %T Neural Jump-Diffusion Temporal Point Processes %A Shuai Zhang %A Chuan Zhou %A Yang Aron Liu %A Peng Zhang %A Xixun Lin %A Zhi-Ming Ma %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-zhang24cm %I PMLR %P 60541--60557 %U https://proceedings.mlr.press/v235/zhang24cm.html %V 235 %X 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.
APA
Zhang, S., Zhou, C., Liu, Y.A., Zhang, P., Lin, X. & Ma, Z.. (2024). Neural Jump-Diffusion Temporal Point Processes. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:60541-60557 Available from https://proceedings.mlr.press/v235/zhang24cm.html.

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