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

TL;DR

This paper demonstrates that Bayesian neural networks can effectively estimate photometric redshifts and their uncertainties for large astronomical surveys like LSST, meeting key scientific requirements.

Contribution

The study introduces the application of Bayesian neural networks for photometric redshift estimation, providing accurate uncertainty quantification and comparison with traditional models.

Findings

BNNs produce reliable redshift uncertainties with good coverage.

BNNs meet two of three LSST photo-z science requirements.

Comparison shows BNNs outperform standard neural networks in uncertainty estimation.

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 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 (NN) 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-$\sigma$ 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 $0 < z < 2.5$.