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

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 1 σ 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.