Amortized Variational Inference of Latent Intensities from Replicated Point Patterns

Abstract:Bayesian inference for latent point process intensities often relies on per-dataset sampling or optimization, making repeated inference computationally expensive. We propose a neural-network-based amortized variational framework that learns a reusable inference rule mapping a variable number of replicated point patterns to a distribution over their shared latent intensity. Trained from event times using the point process likelihood, the model learns an amortized inference rule without ground-truth intensity supervision. At test time, it performs inference of the latent distribution in a forward pass. On synthetic data, additional realizations improve intensity recovery and yield narrower credible intervals with broadly stable coverage. Our method is tested on bicycle-sharing data and achieves the highest mean held-out log likelihood among the evaluated methods while requiring substantially less inference time than the Log-Gaussian Cox Process baseline.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2610.16669 [stat.ML]

(or arXiv:2610.16669v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2610.16669 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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