Flow-Based Delayed Hawkes Process

Chao Yang, Wendi Ren, Shuang Li
Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, PMLR 286:4752-4774, 2025.

Abstract

Multivariate Hawkes processes are classic temporal point process models for event data. These models are simple and parametric in nature, offering interpretability by capturing the triggering effects between event types. However, these parametric models often struggle with low model capacity, limiting their expressive power to capture heterogeneous data patterns influenced by latent variables. In this paper, we propose a simple yet powerful extension: the Flow-based Delayed Hawkes Process, which integrates Normalizing Flows as a generative model to parameterize the Hawkes process. By generating all model parameters through the flow-based network, our approach significantly improves flexibility and expressiveness while preserving interpretability. We provide theoretical guarantees by proving the identifiability of the model parameters and the consistency of the maximum likelihood estimator under mild assumptions. Extensive experiments on both synthetic and real-world datasets show that our model outperforms existing baselines in capturing intricate and heterogeneous event dynamics.

Cite this Paper

BibTeX
@InProceedings{pmlr-v286-yang25d, title = {Flow-Based Delayed Hawkes Process}, author = {Yang, Chao and Ren, Wendi and Li, Shuang}, booktitle = {Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence}, pages = {4752--4774}, year = {2025}, editor = {Chiappa, Silvia and Magliacane, Sara}, volume = {286}, series = {Proceedings of Machine Learning Research}, month = {21--25 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v286/main/assets/yang25d/yang25d.pdf}, url = {https://proceedings.mlr.press/v286/yang25d.html}, abstract = {Multivariate Hawkes processes are classic temporal point process models for event data. These models are simple and parametric in nature, offering interpretability by capturing the triggering effects between event types. However, these parametric models often struggle with low model capacity, limiting their expressive power to capture heterogeneous data patterns influenced by latent variables. In this paper, we propose a simple yet powerful extension: the Flow-based Delayed Hawkes Process, which integrates Normalizing Flows as a generative model to parameterize the Hawkes process. By generating all model parameters through the flow-based network, our approach significantly improves flexibility and expressiveness while preserving interpretability. We provide theoretical guarantees by proving the identifiability of the model parameters and the consistency of the maximum likelihood estimator under mild assumptions. Extensive experiments on both synthetic and real-world datasets show that our model outperforms existing baselines in capturing intricate and heterogeneous event dynamics.} }
Endnote
%0 Conference Paper %T Flow-Based Delayed Hawkes Process %A Chao Yang %A Wendi Ren %A Shuang Li %B Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2025 %E Silvia Chiappa %E Sara Magliacane %F pmlr-v286-yang25d %I PMLR %P 4752--4774 %U https://proceedings.mlr.press/v286/yang25d.html %V 286 %X Multivariate Hawkes processes are classic temporal point process models for event data. These models are simple and parametric in nature, offering interpretability by capturing the triggering effects between event types. However, these parametric models often struggle with low model capacity, limiting their expressive power to capture heterogeneous data patterns influenced by latent variables. In this paper, we propose a simple yet powerful extension: the Flow-based Delayed Hawkes Process, which integrates Normalizing Flows as a generative model to parameterize the Hawkes process. By generating all model parameters through the flow-based network, our approach significantly improves flexibility and expressiveness while preserving interpretability. We provide theoretical guarantees by proving the identifiability of the model parameters and the consistency of the maximum likelihood estimator under mild assumptions. Extensive experiments on both synthetic and real-world datasets show that our model outperforms existing baselines in capturing intricate and heterogeneous event dynamics.
APA
Yang, C., Ren, W. & Li, S.. (2025). Flow-Based Delayed Hawkes Process. Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 286:4752-4774 Available from https://proceedings.mlr.press/v286/yang25d.html.

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