用岭回归改进关联函数拟合：在互相关重建中的应用
Improving Correlation Function Fitting with Ridge Regression: Application to Cross-Correlation Reconstruction
摘要：
互相关技术提供了一种很有前途的途径，用于校准测光红移和使用系统不完整的光谱学来确定红移分布（例如，目前的深光谱调查未能获得30-50%或更多的目标星系的安全红移）。本文改进了Matthews & Newman（2010）提出的红移分布重构方法，将完整的协方差信息加入到我们的关联函数拟合中。关联函数测量在角度或空间仓之间是强协变的，并且在拟合中考虑到这一点可以产生误差的显著减少。然而，在这些计算中使用的协方差矩阵通常是从相对较小的子样本或模拟星表集合（几十个而不是几百个）中确定的，从而导致噪声协方差矩阵，其逆是病态的并且数值不稳定。我们在这里提出了一种称为岭回归的协方差矩阵的调节方法，该方法比大尺度结构研究中常见的其他技术更好地进行反演。我们证明，岭回归显着提高了关联函数参数的测定。然后，我们将这些改进的技术的问题，重建红移分布。通过将完整的协方差信息，应用岭回归，并改变加权的字段获得平均关联函数，我们得到的平均红移分布重建误差的减少高达~40%，与以前的方法相比。在附录中，我们提供了POWERFIT的描述，这是一个IDL代码，用于执行幂律拟合关联函数，并使用我们公开提供的岭回归条件。
英文摘要：
Cross-correlation techniques provide a promising avenue for calibrating photometric redshifts and determining redshift distributions using spectroscopy which is systematically incomplete (e.g., current deep spectroscopic surveys fail to obtain secure redshifts for 30-50% or more of the galaxies targeted). In this paper we improve on the redshift distribution reconstruction methods presented in Matthews & Newman (2010) by incorporating full covariance information into our correlation function fits. Correlation function measurements are strongly covariant between angular or spatial bins, and accounting for this in fitting can yield substantial reduction in errors. However, frequently the covariance matrices used in these calculations are determined from a relatively small set (dozens rather than hundreds) of subsamples or mock catalogs, resulting in noisy covariance matrices whose inversion is ill-conditioned and numerically unstable. We present here a method of conditioning the covariance matrix known as ridge regression which results in a more well behaved inversion than other techniques common in large-scale structure studies. We demonstrate that ridge regression significantly improves the determination of correlation function parameters. We then apply these improved techniques to the problem of reconstructing redshift distributions. By incorporating full covariance information, applying ridge regression, and changing the weighting of fields in obtaining average correlation functions, we obtain reductions in the mean redshift distribution reconstruction error of as much as ~40% compared to previous methods. In an appendix, we provide a description of POWERFIT, an IDL code for performing power-law fits to correlation functions with ridge regression conditioning that we are making publicly available.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
