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.
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BibTeX
@misc{liu2026amortized,
title = {{Amortized Variational Inference of Latent Intensities from Replicated Point Patterns}},
author = {Wenqing Liu and Xenia Miscouridou and Déborah Sulem},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16669},
eprint = {2610.16669},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16669},
}
RIS
TY - UNPB
TI - Amortized Variational Inference of Latent Intensities from Replicated Point Patterns
AU - Wenqing Liu
AU - Xenia Miscouridou
AU - Déborah Sulem
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16669
UR - https://arxiv.org/abs/2610.16669
AB - 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.
ER -