A Scalable Gaussian Process Approach to Shear Mapping with MuyGPs

TL;DR

This paper introduces MuyGPs, a scalable Gaussian Process method for shear mapping in cosmic shear analysis, enabling efficient and accurate inference of matter distribution from billions of measurements.

Contribution

The paper presents a novel linear-scaling Gaussian Process approach, MuyGPs, for shear map construction that avoids cubic computational costs by using nearest-neighbor conditioning.

Findings

Accurately interpolates shear maps from simulations.

Recovers two-point and higher order correlations.

Operates efficiently at the scale of billions of galaxies.

Abstract

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.