Neural Diffusion Intensity Models for Point Process Data
This work addresses the computational bottleneck in point process modeling for researchers and practitioners, offering a scalable alternative to MCMC.
The paper tackled the intractability of nonparametric estimation and posterior inference for Cox processes by introducing Neural Diffusion Intensity Models, a variational framework using neural SDEs, which achieved orders-of-magnitude speedups over MCMC methods while accurately recovering latent intensity dynamics.
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.