Improving Photometric Redshift Estimation for Cosmology with LSST Using Bayesian Neural Networks

Abstract

Abstract We present results exploring the role that probabilistic deep learning models can play in cosmology from large-scale astronomical surveys through photometric redshift (photo-z) estimation. Photo-z uncertainty estimates are critical for the science goals of upcoming large-scale surveys such as the Legacy Survey of Space and Time (LSST); however, common machine learning methods typically provide only point estimates and lack uncertainties on predictions. We turn to Bayesian neural networks (BNNs) as a promising way to provide accurate predictions of redshift values with uncertainty estimates. We have compiled a galaxy data set from the Hyper Suprime-Cam Survey with grizy photometry, which is designed to be a smaller-scale version of large surveys like LSST. We use this data set to investigate the performance of a neural network and a probabilistic BNN for photo-z estimation and evaluate their performance with respect to LSST photo-z science requirements. We also examine the utility of photo-z uncertainties as a means to reduce catastrophic outlier estimates. The BNN outputs the estimate in the form of a Gaussian probability distribution. We use the mean and standard deviation as the redshift estimate and uncertainty. We find that the BNN can produce accurate uncertainties. Using a coverage test, we find excellent agreement with expectation—67.2% of galaxies between 0 < 2.5 have 1σ uncertainties that cover the spectroscopic value. We also include a comparison to alternative machine learning models using the same data. We find the BNN meets two out of three of the LSST photo-z science requirements in the range 0 < z < 2.5.