Neural Diffusion Intensity Models for Point Process Data

2026-02-27

AI Summary

This work addresses the computational challenges of nonparametric posterior inference for latent intensity models in Cox processes, which typically rely on expensive Markov chain Monte Carlo (MCMC) methods that do not scale well. The authors propose a variational inference framework based on Neural Stochastic Differential Equations (Neural SDEs), incorporating filtering enlargement theory—introduced here for the first time in point process modeling—to guarantee that the variational family encompasses the true posterior. An amortized encoder is designed to approximate posterior trajectories efficiently with a single forward pass. Experiments demonstrate that the method accurately recovers latent intensity dynamics on both synthetic and real-world data, achieving speedups of several orders of magnitude over MCMC while maintaining theoretical rigor and computational scalability.

Technology Category

• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Cox processes model overdispersed point process data via a latent stochastic intensity, but both nonparametric estimation of the intensity model and posterior inference over intensity paths are typically intractable, relying on expensive MCMC methods. We introduce Neural Diffusion Intensity Models, a variational framework for Cox processes driven by neural 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 guarantees the variational family contains the true posterior, so that ELBO maximization coincides with maximum likelihood estimation under sufficient model capacity. We design 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 pass. 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.

Problem

• Cox processes
• latent intensity
• posterior inference
• point process data
• nonparametric estimation

Innovation

• Neural SDE
• Cox process
• Variational inference
• Enlargement of filtrations
• Amortized encoder