# Large-Scale Cox Process Inference using Variational Fourier Features

arXiv: https://arxiv.org/abs/1804.01016 · HTML: https://mlsanity.com/paper/1804.01016/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2018.

## Built on by (most cited first, 8 of 8)

- [Variational Nearest Neighbor Gaussian Process](https://mlsanity.com/paper/2202.01694/) (2022)
- [Sensing Cox Processes via Posterior Sampling and Positive Bases](https://mlsanity.com/paper/2110.11181/) (2021)
- [The Minecraft Kernel: Modelling correlated Gaussian Processes in the Fourier domain](https://mlsanity.com/paper/2103.06950/) (2021)
- [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)
- [Latent variable model for high-dimensional point process with structured missingness](https://mlsanity.com/paper/2402.05758/) (2024)
- [K2IE: Kernel Method-based Kernel Intensity Estimators for Inhomogeneous Poisson Processes](https://mlsanity.com/paper/2505.24704/) (2025)

## Abstract (arXiv)

Gaussian process modulated Poisson processes provide a flexible framework for modelling spatiotemporal point patterns. So far this had been restricted to one dimension, binning to a pre-determined grid, or small data sets of up to a few thousand data points. Here we introduce Cox process inference based on Fourier features. This sparse representation induces global rather than local constraints on the function space and is computationally efficient. This allows us to formulate a grid-free approximation that scales well with the number of data points and the size of the domain. We demonstrate that this allows MCMC approximations to the non-Gaussian posterior. We also find that, in practice, Fourier features have more consistent optimization behavior than previous approaches. Our approximate Bayesian method can fit over 100,000 events with complex spatiotemporal patterns in three dimensions on a single GPU.