# Gaussian Process Modulated Cox Processes under Linear Inequality Constraints

arXiv: https://arxiv.org/abs/1902.10974 · HTML: https://mlsanity.com/paper/1902.10974/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2019.

## Built on by (most cited first, 4 of 4)

- [Sensing Cox Processes via Posterior Sampling and Positive Bases](https://mlsanity.com/paper/2110.11181/) (2021)
- [High-dimensional additive Gaussian processes under monotonicity constraints](https://mlsanity.com/paper/2205.08528/) (2022)
- [Aligned Multi-Task Gaussian Process](https://mlsanity.com/paper/2110.15761/) (2021)
- [Exact Bayesian Gaussian Cox Processes Using Random Integral](https://mlsanity.com/paper/2406.19722/) (2024)

## Abstract (arXiv)

Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions that do not have a closed form or that are restricted to specific covariance functions. We introduce a novel finite approximation of GP-modulated Cox processes where positiveness conditions can be imposed directly on the GP, with no restrictions on the covariance function. Our approach can also ensure other types of inequality constraints (e.g. monotonicity, convexity), resulting in more versatile models that can be used for other classes of point processes (e.g. renewal processes). We demonstrate on both synthetic and real-world data that our framework accurately infers the intensity functions. Where monotonicity is a feature of the process, our ability to include this in the inference improves results.