Calibrated Photometric Redshift Distributions for LSST: A Conditional Density Estimation Approach with Correction for Spectroscopic Selection Bias

Abstract: Accurate and well-calibrated photometric redshift (photo-z) probability distributions are essential for cosmological analyses with the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST). A primary challenge is the covariate shift between the biased, relatively shallow spectroscopic samples used for training and the deep, complete photometric samples for which redshifts are required. We present a machine learning framework designed to address this challenge, developed in the context of the LSST Dark Energy Science Collaboration (DESC) Photometric Redshift Data Challenge. Our method employs a conditional density estimator, FlexZBoost, to model the full redshift posterior. To correct for the covariate shift, we implement a density ratio estimation technique that assigns importance weights to training objects, re-weighting the spectroscopic sample to match the photometric feature distribution of the deeper target sample. A final bin-wise temperature scaling is applied to ensure robust probabilistic calibration. Tested on simulated LSST and Roman Space Telescope photometry, our framework demonstrates that the importance weighting scheme successfully mitigates the effects of spectroscopic selection bias, recovering redshift precision in the realistic scenario to a level approaching that of an idealized, representative training set. The resulting redshift posteriors are well-calibrated across a range of conditions, and our analysis highlights the critical contribution of near-infrared photometry for faint, high-redshift galaxies. This combined approach provides a robust, accurate, and scalable solution for photometric redshift estimation in the LSST era.

Subjects:	astro-ph.IM; astro-ph.CO; cs.LG
Cite as:	PX:2604.00034