Neural Diffusion Intensity Models for Point Process Data

TL;DR

This paper introduces Neural Diffusion Intensity Models, a variational approach using neural SDEs for efficient and accurate inference of latent intensities in Cox processes, outperforming traditional MCMC methods.

Contribution

It presents a novel neural SDE-based variational framework for Cox processes, enabling tractable inference and maximum likelihood estimation with a single forward pass.

Findings

Accurately recovers latent intensity dynamics.

Achieves significant speedups over MCMC methods.

Validates effectiveness on synthetic and real data.

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.