How to use GP: Effects of the mean function and hyperparameter selection on Gaussian Process regression

TL;DR

This paper investigates how the choice of mean function and hyperparameters influences Gaussian Process regression in cosmology, proposing marginalization techniques to improve the robustness of supernova distance reconstructions.

Contribution

It introduces a method to marginalize over mean functions and hyperparameters, reducing bias and dependence in Gaussian Process cosmological reconstructions.

Findings

Mean function choice impacts physical plausibility of results

Marginalization reduces bias in reconstructions

Method remains unbiased across different kernel functions

Abstract

Gaussian processes have been widely used in cosmology to reconstruct cosmological quantities in a model-independent way. However, the validity of the adopted mean function and hyperparameters, and the dependence of the results on the choice have not been well explored. In this paper, we study the effects of the underlying mean function and the hyperparameter selection on the reconstruction of the distance moduli from type Ia supernovae. We show that the choice of an arbitrary mean function affects the reconstruction: a zero mean function leads to unphysical distance moduli and the best-fit LCDM to biased reconstructions. We propose to marginalize over a family of mean functions and over the hyperparameters to effectively remove their impact on the reconstructions. We further explore the validity and consistency of the results considering different kernel functions and show that our method is unbiased.