# Amortized Variational Inference of Latent Intensities from Replicated Point Patterns

arXiv: https://arxiv.org/abs/2610.16669 · HTML: https://mlsanity.com/paper/2610.16669/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 28 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Conditional Neural Processes](https://mlsanity.com/paper/1807.01613/) (2018)
- [Transformer Hawkes Process](https://mlsanity.com/paper/2002.09291/) (2020)
- [Fully Neural Network based Model for General Temporal Point Processes](https://mlsanity.com/paper/1905.09690/) (2019)
- [Variational Inference for Gaussian Process Modulated Poisson Processes](https://mlsanity.com/paper/1411.0254/) (2014)
- [Meta-Amortized Variational Inference and Learning](https://mlsanity.com/paper/1902.01950/) (2019)
- [Efficient Bayesian Inference of Sigmoidal Gaussian Cox Processes](https://mlsanity.com/paper/1808.00831/) (2018)
- [Meta Temporal Point Processes](https://mlsanity.com/paper/2301.12023/) (2023)
- [In-Context Learning of Temporal Point Processes with Foundation Inference Models](https://mlsanity.com/paper/2509.24762/) (2025)
- [Deep Random Splines for Point Process Intensity Estimation of Neural Population Data](https://mlsanity.com/paper/1903.02610/) (2019)
- [Meta-Learning for Neural Network-based Temporal Point Processes](https://mlsanity.com/paper/2401.15846/) (2024)
- [Neural Diffusion Intensity Models for Point Process Data](https://mlsanity.com/paper/2602.24083/) (2026)

## Abstract (arXiv)

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.