Measuring the Probabilistic Photometric Redshifts of X-ray Quasars Based on the Quantile Regression of Ensembles of Decision Trees

Abstract

We present empirical machine learning algorithms for measuring the probabilistic photometric redshifts (photo-z) of X-ray quasars based on the quantile regression of ensembles of decision trees. Relying on the data of present-day photometric sky surveys (e.g., SDSS, GALEX, WISE, UKIDSS, 2MASS, FIRST), the proposed methods allow one to make high-quality photo-z point predictions for extragalactic objects, to estimate the confidence intervals, and to reconstruct the full probability distribution functions for all predictions. The quality of photo-z predictions has been tested on samples of X-ray quasars from the 1RASS and 3XMM DR7 surveys, which have spectroscopic redshift measurements in the SDSS DR14Q catalog. The proposed approaches have shown the following accuracy (the metrics are the normalized median absolute deviation σNMAD and the percentage of outliers n_>0.15): σ_NMAD, n_>0.15 = 0.043, 12% (SDSS + WISE), 0.037, 8% (SDSS + WISE + GALEX) and 0.032, 8.6% (SDSS + WISE + GALEX + UKIDSS) on the RASS sample; σ_NMAD, n_>0.15 = 0.054, 13% (SDSS + WISE), 0.045, 7.6% (SDSS + WISE + GALEX), and 0.037, 6.6% (SDSS + WISE + GALEX + UKIDSS) on the 3XMM sample. The presented photo-z algorithms will become an important tool for analyzing the multi-wavelength data on X-ray quasars in the forthcoming Spectrum–Roentgen–Gamma sky survey.