Estimating redshift distributions of Fermi blazars with multiple machine-learning models
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 to provide predictive redshift probability distributions with quantified uncertainties for all blazars without measured redshifts. We construct an ensemble of 35 machine-learning regression models in the $1/(1+z)$ space. Predictions from individual models are combined to build non-parametric redshift probability density functions (PDFs) for each source, allowing an explicit characterization of predictive uncertainty. The source-level PDFs are subsequently stacked to derive population-level redshift distributions. Across the diverse models within our framework, we find comparable predictive performance, indicating a feature-limited performance plateau. We compile a catalog of predictive redshift distributions for 1,590 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 1,590 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 ensembling in astronomical data analysis.