GPZ: non-stationary sparse Gaussian processes for heteroscedastic uncertainty estimation in photometric redshifts
GPZ: non-stationary sparse Gaussian processes for heteroscedastic uncertainty estimation in photometric redshifts
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DOI：
10.1093/mnras/stw1618
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发表时间：
2016-10-11
影响因子：
4.8
通讯作者：
Roberts, Stephen J.
中科院分区：
文献类型：
--
作者：
Almosallam, Ibrahim A.;Jarvis, Matt J.;Roberts, Stephen J.
下一代宇宙学实验将被要求使用光度红移，而不是光谱红移。因此，获得准确和特征明确的光度学红移分布对于欧几里得、大型天文观测望远镜和平方公里阵列至关重要。然而，确定准确的方差预测和单点估计是至关重要的，因为它们可以用于为特定的实验优化星系样本(例如弱透镜、重子声振荡、超新星)，在星系样本的完整性和可靠性之间进行权衡。光度和红移测量中的各种不确定度来源给任何模型所希望达到的精度设定了一个下限。与估计相关的内在不确定性通常是非均匀的和依赖于输入的，在统计学上通常被称为异方差噪声。然而，现有的方法容易受到离群点的影响，并且没有考虑到非均匀数据密度引起的方差，并且在大多数情况下需要手动调整许多参数。在本文中，我们提出了一种贝叶斯机器学习方法，该方法针对光度学红移(GPZ)的预测均值和方差联合优化模型，称为高斯过程。模型的预测方差既考虑了数据密度的方差，也考虑了光度学噪声。使用斯隆数字天空调查(SDSS)的DR12数据，我们的方法在照片z估计及其相关方差方面远远优于其他机器学习方法，如TPZ和ANNZ2。我们提供了可从https://github.com/OxfordML/GPz.下载的MatLab和Python语言实现
The next generation of cosmology experiments will be required to use photometric redshifts rather than spectroscopic redshifts. Obtaining accurate and well-characterized photometric redshift distributions is therefore critical for Euclid, the Large Synoptic Survey Telescope and the Square Kilometre Array. However, determining accurate variance predictions alongside single point estimates is crucial, as they can be used to optimize the sample of galaxies for the specific experiment (e.g. weak lensing, baryon acoustic oscillations, supernovae), trading off between completeness and reliability in the galaxy sample. The various sources of uncertainty in measurements of the photometry and redshifts put a lower bound on the accuracy that any model can hope to achieve. The intrinsic uncertainty associated with estimates is often non-uniform and input-dependent, commonly known in statistics as heteroscedastic noise. However, existing approaches are susceptible to outliers and do not take into account variance induced by non-uniform data density and in most cases require manual tuning of many parameters. In this paper, we present a Bayesian machine learning approach that jointly optimizes the model with respect to both the predictive mean and variance we refer to as Gaussian processes for photometric redshifts (GPZ). The predictive variance of the model takes into account both the variance due to data density and photometric noise. Using the Sloan Digital Sky Survey (SDSS) DR12 data, we show that our approach substantially outperforms other machine learning methods for photo-z estimation and their associated variance, such as TPZ and ANNZ2. We provide a MATLAB and PYTHON implementations that are available to download at https://github.com/OxfordML/GPz.