Neural Diffusion Intensity Models for Point Process Data

Xinlong Du, Harsha Honnappa, Vinayak Rao
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:1448-1473, 2026.

Abstract

Cox processes model overdispersed point process data via a latent stochastic intensity, but both estimation of the nonparametric intensity model and posterior inference over intensity paths are generally intractable, relying on computationally-heavy {MCMC} methods. We introduce Neural Diffusion Intensity Models, a variational inference framework for Cox processes driven by neural stochastic differential equations (SDEs). Our key theoretical result, based on enlargement of filtrations, shows that conditioning on point process observations preserves the diffusion structure of the latent intensity with an explicit drift correction. This provides guidance on how to choose an appropriate variational family so that {ELBO} maximization coincides with maximum likelihood estimation under sufficient model capacity. We provide an amortized encoder architecture that maps variable-length event sequences to posterior intensity paths by simulating the drift-corrected SDE, replacing repeated {MCMC} runs with a single forward SDE simulation. Experiments on synthetic and real-world data demonstrate accurate recovery of latent intensity dynamics and posterior paths, with orders-of-magnitude speedups over {MCMC}-based methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-du26a, title = {Neural Diffusion Intensity Models for Point Process Data}, author = {Du, Xinlong and Honnappa, Harsha and Rao, Vinayak}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {1448--1473}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/du26a/du26a.pdf}, url = {https://proceedings.mlr.press/v337/du26a.html}, abstract = {Cox processes model overdispersed point process data via a latent stochastic intensity, but both estimation of the nonparametric intensity model and posterior inference over intensity paths are generally intractable, relying on computationally-heavy {MCMC} methods. We introduce Neural Diffusion Intensity Models, a variational inference framework for Cox processes driven by neural stochastic differential equations (SDEs). Our key theoretical result, based on enlargement of filtrations, shows that conditioning on point process observations preserves the diffusion structure of the latent intensity with an explicit drift correction. This provides guidance on how to choose an appropriate variational family so that {ELBO} maximization coincides with maximum likelihood estimation under sufficient model capacity. We provide an amortized encoder architecture that maps variable-length event sequences to posterior intensity paths by simulating the drift-corrected SDE, replacing repeated {MCMC} runs with a single forward SDE simulation. Experiments on synthetic and real-world data demonstrate accurate recovery of latent intensity dynamics and posterior paths, with orders-of-magnitude speedups over {MCMC}-based methods.} }
Endnote
%0 Conference Paper %T Neural Diffusion Intensity Models for Point Process Data %A Xinlong Du %A Harsha Honnappa %A Vinayak Rao %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-du26a %I PMLR %P 1448--1473 %U https://proceedings.mlr.press/v337/du26a.html %V 337 %X Cox processes model overdispersed point process data via a latent stochastic intensity, but both estimation of the nonparametric intensity model and posterior inference over intensity paths are generally intractable, relying on computationally-heavy {MCMC} methods. We introduce Neural Diffusion Intensity Models, a variational inference framework for Cox processes driven by neural stochastic differential equations (SDEs). Our key theoretical result, based on enlargement of filtrations, shows that conditioning on point process observations preserves the diffusion structure of the latent intensity with an explicit drift correction. This provides guidance on how to choose an appropriate variational family so that {ELBO} maximization coincides with maximum likelihood estimation under sufficient model capacity. We provide an amortized encoder architecture that maps variable-length event sequences to posterior intensity paths by simulating the drift-corrected SDE, replacing repeated {MCMC} runs with a single forward SDE simulation. Experiments on synthetic and real-world data demonstrate accurate recovery of latent intensity dynamics and posterior paths, with orders-of-magnitude speedups over {MCMC}-based methods.
APA
Du, X., Honnappa, H. & Rao, V.. (2026). Neural Diffusion Intensity Models for Point Process Data. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:1448-1473 Available from https://proceedings.mlr.press/v337/du26a.html.

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