# Marginalizing Gaussian Process Hyperparameters using Sequential Monte Carlo

arXiv: https://arxiv.org/abs/1502.01908 · HTML: https://mlsanity.com/paper/1502.01908/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Feb 2015.

## Built on by (most cited first, 6 of 6)

- [Mixtures of Gaussian Process Experts with SMC2](https://mlsanity.com/paper/2208.12830/) (2022)
- [Bayesian grey-box identification of nonlinear convection effects in heat transfer dynamics](https://mlsanity.com/paper/2407.01226/) (2024)
- [Bayesian autoregression to optimize temporal Mat'ern kernel Gaussian process hyperparameters](https://mlsanity.com/paper/2508.09792/) (2025)
- [A Bayesian Approach To Graph Partitioning](https://mlsanity.com/paper/2204.12927/) (2022)
- [Online Student-t Processes with an Overall-local Scale Structure for Modelling Non-stationary Data](https://mlsanity.com/paper/2311.00564/) (2023)
- [Robust Inference of Dynamic Covariance Using Wishart Processes and Sequential Monte Carlo](https://mlsanity.com/paper/2406.04796/) (2024)

## Abstract (arXiv)

Gaussian process regression is a popular method for non-parametric probabilistic modeling of functions. The Gaussian process prior is characterized by so-called hyperparameters, which often have a large influence on the posterior model and can be difficult to tune. This work provides a method for numerical marginalization of the hyperparameters, relying on the rigorous framework of sequential Monte Carlo. Our method is well suited for online problems, and we demonstrate its ability to handle real-world problems with several dimensions and compare it to other marginalization methods. We also conclude that our proposed method is a competitive alternative to the commonly used point estimates maximizing the likelihood, both in terms of computational load and its ability to handle multimodal posteriors.