标题： 一种可扩展的高斯过程用于剪切映射的MuyGPs方法 显示英文标题

标题： A Scalable Gaussian Process Approach to Shear Mapping with MuyGPs

摘要： 宇宙剪切分析是理解宇宙时间内结构增长的重要组成部分，这反过来为我们提供了关于暗能量性质的信息。 传统方法生成的\emph{剪切图}可以让我们推断宇宙中的物质分布。 然而，目前用于生成这些地图的方法（例如，Kaiser-Squires反演）实施起来很棘手，并可能引入偏差。 最近的替代方法为透镜势构建了一个空间过程先验，这使得可以根据透镜剪切测量值推断出汇聚和剪切参数。 然而，实现这些空间过程在观测数量上呈三次方增长——对于即将进行的预计会产生数十亿相关测量值的调查来说，这是一个无法接受的开销。 因此，我们提出了一种线性尺度的剪切图构造替代方案，使用一种名为 MuyGPs 的可扩展高斯过程（GP）先验。 MuyGPs 通过仅对最近邻点进行条件插值来避免三次方增长，并使用批量留一法交叉验证来拟合超参数。 我们使用来自 N 体模拟的一组光线追踪结果证明了我们的方法可以准确地插值剪切图，并恢复两点和更高阶的相关性。 我们还表明可以在高性能计算平台上以数十亿个星系的规模执行这些操作。 显示英文摘要

摘要： Analysis of cosmic shear is an integral part of understanding structure growth across cosmic time, which in-turn provides us with information about the nature of dark energy. Conventional methods generate \emph{shear maps} from which we can infer the matter distribution in the universe. Current methods (e.g., Kaiser-Squires inversion) for generating these maps, however, are tricky to implement and can introduce bias. Recent alternatives construct a spatial process prior for the lensing potential, which allows for inference of the convergence and shear parameters given lensing shear measurements. Realizing these spatial processes, however, scales cubically in the number of observations - an unacceptable expense as near-term surveys expect billions of correlated measurements. Therefore, we present a linearly-scaling shear map construction alternative using a scalable Gaussian Process (GP) prior called MuyGPs. MuyGPs avoids cubic scaling by conditioning interpolation on only nearest-neighbors and fits hyperparameters using batched leave-one-out cross validation. We use a suite of ray-tracing results from N-body simulations to demonstrate that our method can accurately interpolate shear maps, as well as recover the two-point and higher order correlations. We also show that we can perform these operations at the scale of billions of galaxies on high performance computing platforms.