# Fast Bayesian Intensity Estimation for the Permanental Process

arXiv: https://arxiv.org/abs/1701.03535 · HTML: https://mlsanity.com/paper/1701.03535/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jan 2017.

## Built on by (most cited first, 10 of 10)

- [Squared Neural Families: A New Class of Tractable Density Models](https://mlsanity.com/paper/2305.13552/) (2023)
- [Exact, Fast and Expressive Poisson Point Processes via Squared Neural Families](https://mlsanity.com/paper/2402.09608/) (2024)
- [Bayesian Optimization through Gaussian Cox Process Models for Spatio-temporal Data](https://mlsanity.com/paper/2401.14544/) (2024)
- [Sensing Cox Processes via Posterior Sampling and Positive Bases](https://mlsanity.com/paper/2110.11181/) (2021)
- [Advances in Temporal Point Processes: Bayesian, Neural, and LLM Approaches](https://mlsanity.com/paper/2501.14291/) (2025)
- [Nonstationary Sparse Spectral Permanental Process](https://mlsanity.com/paper/2410.03581/) (2024)
- [Squared families: Searching beyond regular probability models](https://mlsanity.com/paper/2503.21128/) (2025)
- [Spatio-temporal extreme event modeling of terror insurgencies](https://mlsanity.com/paper/2110.08363/) (2021)
- [K2IE: Kernel Method-based Kernel Intensity Estimators for Inhomogeneous Poisson Processes](https://mlsanity.com/paper/2505.24704/) (2025)
- [An RKHS Framework for Fixed Effects in Permanental Process Models](https://mlsanity.com/paper/2608.17908/) (2026)

## Abstract (arXiv)

The Cox process is a stochastic process which generalises the Poisson process by letting the underlying intensity function itself be a stochastic process. In this paper we present a fast Bayesian inference scheme for the permanental process, a Cox process under which the square root of the intensity is a Gaussian process. In particular we exploit connections with reproducing kernel Hilbert spaces, to derive efficient approximate Bayesian inference algorithms based on the Laplace approximation to the predictive distribution and marginal likelihood. We obtain a simple algorithm which we apply to toy and real-world problems, obtaining orders of magnitude speed improvements over previous work.