论文标题
如何使用GP：平均函数和超参数选择对高斯过程回归的影响
How to use GP: Effects of the mean function and hyperparameter selection on Gaussian Process regression
论文作者
论文摘要
高斯过程已被广泛用于宇宙学中，以独立的方式重建宇宙学数量。但是，所采用的平均函数和超参数的有效性以及结果对选择的依赖性尚未得到很好的探索。在本文中，我们研究了基本平均函数和超参数选择对IA型超新星距离模量重建的影响。我们表明，任意均值函数的选择会影响重建：零均值函数导致非物理距离模量和对偏置重建的最佳拟合LCDM。我们建议将平均功能家族和超参数的家庭边缘化，以有效地消除其对重建的影响。我们进一步探讨了考虑不同核函数的结果的有效性和一致性，并表明我们的方法是公正的。
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.
