The identification of physically associated kiloparsec-scale quasar pairs is important for understanding galaxy evolution, the growth of supermassive black holes, and co-evolution of supermassive black holes and their host galaxies. However, their intrinsic rarity and high contamination from stellar superpositions and projected alignments in photometric catalogues necessitate efficient selection methods. This challenge is amplified as wide-field imaging surveys such as the Legacy Survey of Space and Time (LSST) and will discover vast numbers of quasar candidates, most lacking immediate spectroscopic follow-up, making accurate photometric redshifts (photo-z) essential for pre-selection. Euclid This work aims to develop a robust machine learning framework to produce accurate photo-z point estimates and well-calibrated probability density functions (PDFs) for quasars. The primary application is to systematically identify high-probability quasar pair candidates within the MGQPC (quasar pair candidates derived from the cross-match of MQC and Gaia) catalogue by assessing the redshift consistency of pair components. We constructed two large, spectroscopically confirmed quasar samples with multi-wavelength photometry: an SDSS-based sample (KSTS) and a DESI-LS-based sample (KSTD). We employed the algorithm for point-estimate photo-z regression and the framework for full photo-z PDF estimation. A feature selection process guided by SHAP (SHapley Additive exPlanations) was implemented to identify the most predictive photometric features, including colours and magnitudes from optical (e. g. u, g, r, i, z, G, G_ CatBoost FlexZBoost BP, G_ RP) and infrared (W1, W2) bands. Our photo-z workflow achieves a robust performance, with a normalised median absolute deviation of σ_ NMAD =0. 036 and an outlier fraction of 5. 6% on the test sample. The resulting photo-z PDFs are well calibrated, as verified by probability integral transform diagnostics. Control tests indicate that the better performance of the SDSS-based sample is primarily attributable to the inclusion of the u band, although survey-dependent photometric differences in LS10, including bright-source systematics, may also play a contributing role. Applying this trained model to the MGQPC catalogue, we identified 185 high-probability quasar pair candidates based on the consistency between their photo-z estimates. This candidate list included 20 systems subsequently confirmed as genuine physical pairs by independent spectroscopic observations. We demonstrate that modern machine learning techniques, combining gradient-boosted trees for point estimates and conditional density estimation for PDFs, can deliver precise and reliable photo-zs for quasars. This enables the efficient filtering and prioritisation of rare quasar pairs from large photometric catalogues. The resulting photo-z catalogue for the MGQPC provides a valuable resource for future spectroscopic follow-up campaigns to study dual supermassive black holes and their co-evolution.
Zhu et al. (Mon,) studied this question.