Photometric selection and redshifts for quasars in the Kilo-Degree Survey Data Release 4

We present a catalog of quasars with their corresponding redshifts derived from the photometric Kilo-Degree Survey (KiDS) Data Release 4. We achieved it by training machine learning (ML) models, using optical ugri and near-infrared ZYJHK(s) bands, on objects known from Sloan Digital Sky Survey (SDSS) spectroscopy. We define inference subsets from the 45 million objects of the KiDS photometric data limited to 9-band detections, based on a feature space built from magnitudes and their combinations. We show that projections of the high-dimensional feature space on two dimensions can be successfully used, instead of the standard color-color plots, to investigate the photometric estimations, compare them with spectroscopic data, and efficiently support the process of building a catalog. The model selection and fine-tuning employs two subsets of objects: those randomly selected and the faintest ones, which allowed us to properly fit the bias versus variance trade-off. We tested three ML models: random forest (RF), XGBoost (XGB), and artificial neural network (ANN). We find that XGB is the most robust and straightforward model for classification, while ANN performs the best for combined classification and redshift. The ANN inference results are tested using number counts, Gaia parallaxes, and other quasar catalogs that are external to the training set. Based on these tests, we derived the minimum classification probability for quasar candidates which provides the best purity versus completeness trade-off: p(QSO(cand)) > 0.9 for r<22 and p(QSO(cand)) > 0.98 for 22<r<23.5. We find 158 000 quasar candidates in the safe inference subset (r<22) and an additional 185 000 candidates in the reliable extrapolation regime (22<r<23.5). Test-data purity equals 97% and completeness is 94%; the latter drops by 3% in the extrapolation to data fainter by one magnitude than the training set. The photometric redshifts were derived with ANN and modeled with Gaussian uncertainties. The test-data redshift error (mean and scatter) equals 0.009 +/- 0.12 in the safe subset and -0.0004 +/- 0.19 in the extrapolation, averaged over a redshift range of 0.14<z<3.63 (first and 99th percentiles). Our success of the extrapolation challenges the way that models are optimized and applied at the faint data end. The resulting catalog is ready for cosmology and active galactic nucleus (AGN) studies.