Amortized Variational Inference of Latent Intensities from Replicated Point Patterns

Bayesian inference for latent point process intensities often relies on per-dataset sampling or optimization, making repeated inference computationally expensive. We introduce an amortized variational framework based on a Neural Process for replicated point patterns, where a variable-size set of realizations shares a latent intensity. Trained from event times using the point process likelihood, the model learns an amortized inference rule that maps these realizations to a variational distribution over their shared intensity, 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. On bicycle-sharing data, our method achieves the highest mean held-out log likelihood among the evaluated approaches. It also requires substantially less inference time than the LGCP baseline in our experiments.