Estimating redshift distributions of Fermi blazars with multiple machine-learning models

Abstract

Approximately half of the Fermi-LAT-detected blazars lack spectroscopic redshift measurements, which limits population studies and investigations of the cosmological evolution of the gamma-ray blazar population. We aim to develop a multi-model ensemble framework to systematically evaluate the performance of machine-learning models for blazar redshift estimation and provide predictive redshift probability distributions with quantified uncertainties for all blazars with unknown redshifts. We constructed an ensemble of 35 machine-learning regression models in the space. We combined predictions from the individual models to build nonparametric redshift probability density functions (PDFs) for each source, thereby explicitly characterizing the predictive uncertainty. We then stacked the source-level PDFs to derive population-level redshift distributions. We find comparable predictive performance across the diverse models within our framework, indicating a feature-limited performance plateau. We compiled a catalog of predictive redshift distributions for 1590 blazars without measured redshifts. The stacked PDFs recover the characteristic double-peaked redshift structure of blazars without using source-class labels. For blazar candidates of uncertain type, the predicted redshift distribution exhibits a bimodal structure, suggesting a slightly larger contribution from FSRQ-like sources. Our multi-model statistical framework achieves competitive predictive performance while retaining faint sources. We provide predicted redshift distributions with quantified uncertainties for 1590 blazars without measured redshifts, offering improved support for population and evolutionary studies. More broadly, this approach highlights the practical value of uncertainty-aware multi-model regression ensembles in astronomical data analysis.