Noise Estimation in Gaussian Process Regression

TL;DR

This paper introduces an efficient method for estimating noise and covariance hyperparameters in Gaussian process regression by reducing the problem to univariate root-finding and providing bounds for the likelihood function.

Contribution

The authors propose a novel computational approach that simplifies hyperparameter estimation in Gaussian process models, improving efficiency and robustness over traditional methods.

Findings

Method reduces hyperparameter estimation to univariate root-finding.

Provides bounds and asymptotes for the marginal likelihood function.

Demonstrates computational advantages and robustness through numerical examples.

Abstract

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.