# Variational Inference for Gaussian Process Modulated Poisson Processes

arXiv: https://arxiv.org/abs/1411.0254 · HTML: https://mlsanity.com/paper/1411.0254/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2014.

## Built on by (most cited first, 26 of 26)

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- [Heterogeneous Multi-Task Gaussian Cox Processes](https://mlsanity.com/paper/2308.15364/) (2023)
- [Inference and Sampling of Point Processes from Diffusion Excursions](https://mlsanity.com/paper/2306.00762/) (2023)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Causal Modeling of Policy Interventions From Sequences of Treatments and Outcomes](https://mlsanity.com/paper/2209.04142/) (2022)
- [Nonstationary Sparse Spectral Permanental Process](https://mlsanity.com/paper/2410.03581/) (2024)
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- [New Bounds for Sparse Variational Gaussian Processes](https://mlsanity.com/paper/2502.08730/) (2025)
- [Nonlinear Hawkes Process with Gaussian Process Self Effects](https://mlsanity.com/paper/2105.09618/) (2021)
- [Temporal Causal Mediation through a Point Process: Direct and Indirect Effects of Healthcare Interventions](https://mlsanity.com/paper/2306.09656/) (2023)
- [Latent variable model for high-dimensional point process with structured missingness](https://mlsanity.com/paper/2402.05758/) (2024)
- [Squared families: Searching beyond regular probability models](https://mlsanity.com/paper/2503.21128/) (2025)
- [STACI: Spatio-Temporal Aleatoric Conformal Inference](https://mlsanity.com/paper/2505.21658/) (2025)
- [Survival Analysis of the Compressor Station Based on Hawkes Process with Weibull Base Intensity](https://mlsanity.com/paper/2112.13581/) (2021)
- [Modelling financial volume curves with hierarchical Poisson processes](https://mlsanity.com/paper/2406.19402/) (2024)
- [Exact Bayesian Gaussian Cox Processes Using Random Integral](https://mlsanity.com/paper/2406.19722/) (2024)
- [Unsupervised Event Outlier Detection in Continuous Time](https://mlsanity.com/paper/2411.16427/) (2024)
- [K2IE: Kernel Method-based Kernel Intensity Estimators for Inhomogeneous Poisson Processes](https://mlsanity.com/paper/2505.24704/) (2025)
- [A Semiparametric Discrete Hawkes Model with a Collapsed Gaussian-Process Prior](https://mlsanity.com/paper/2509.21996/) (2025)
- [Kronecker-Structured Nonparametric Spatiotemporal Point Processes](https://mlsanity.com/paper/2603.23746/) (2026)
- [Arbitrarily Conditioned Hierarchical Flows for Spatiotemporal Events](https://mlsanity.com/paper/2605.01226/) (2026)
- [Amortized Variational Inference of Latent Intensities from Replicated Point Patterns](https://mlsanity.com/paper/2610.16669/) (2026)

## Abstract (arXiv)

We present the first fully variational Bayesian inference scheme for continuous Gaussian-process-modulated Poisson processes. Such point processes are used in a variety of domains, including neuroscience, geo-statistics and astronomy, but their use is hindered by the computational cost of existing inference schemes. Our scheme: requires no discretisation of the domain; scales linearly in the number of observed events; and is many orders of magnitude faster than previous sampling based approaches. The resulting algorithm is shown to outperform standard methods on synthetic examples, coal mining disaster data and in the prediction of Malaria incidences in Kenya.