# Noise Estimation in Gaussian Process Regression

arXiv: https://arxiv.org/abs/2206.09976 · HTML: https://mlsanity.com/paper/2206.09976/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 80 references that are in the map.
- First posted on arXiv 20 Jun 2022.

## Builds on (most cited first, 3 of 3)

- [Distributed Gaussian Processes](https://mlsanity.com/paper/1502.02843/) (2015)
- [Cross-Covariance Functions for Multivariate Geostatistics](https://mlsanity.com/paper/1507.08017/) (2015)
- [Single Nugget Kriging](https://mlsanity.com/paper/1507.05128/) (2015)

## Built on by (most cited first, 2 of 2)

- [A Singular Woodbury and Pseudo-Determinant Matrix Identities and Application to Gaussian Process Regression](https://mlsanity.com/paper/2207.08038/) (2022)
- [GpFlash: Maximizing Speed and Minimizing Memory for Gaussian Process Training and Prediction](https://mlsanity.com/paper/2610.16861/) (2026)

## Abstract (arXiv)

We develop a computational procedure to estimate the covariance hyperparameters for semiparametric Gaussian process regression models with additive noise. Namely, the presented method can be used to efficiently estimate the variance of the correlated error, and the variance of the noise based on maximizing a marginal likelihood function. Our method involves suitably reducing the dimensionality of the hyperparameter space to simplify the estimation procedure to a univariate root-finding problem. Moreover, we derive bounds and asymptotes of the marginal likelihood function and its derivatives, which are useful to narrowing the initial range of the hyperparameter search. Using numerical examples, we demonstrate the computational advantages and robustness of the presented approach compared to traditional parameter optimization.