# Efficient Bayesian Inference for a Gaussian Process Density Model

arXiv: https://arxiv.org/abs/1805.11494 · HTML: https://mlsanity.com/paper/1805.11494/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2018.

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

- [Nonlinear Hawkes Processes in Time-Varying System](https://mlsanity.com/paper/2106.04844/) (2021)
- [Federated Neural Nonparametric Point Processes](https://mlsanity.com/paper/2410.05637/) (2024)
- [Goal-oriented adaptive sampling under random field modelling of response probability distributions](https://mlsanity.com/paper/2102.07612/) (2021)
- [Nonlinear Hawkes Process with Gaussian Process Self Effects](https://mlsanity.com/paper/2105.09618/) (2021)

## Abstract (arXiv)

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent P'olya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's Gaussian process prior. The augmented posterior allows for efficient inference by Gibbs sampling and an approximate variational mean field approach. For the latter we utilise sparse GP approximations to tackle the infinite dimensionality of the problem. The performance of both algorithms and comparisons with other density estimators are demonstrated on artificial and real datasets with up to several thousand data points.