Boost recall in quasi-stellar object selection from highly imbalanced photometric datasets

Context. The identification of bright quasi-stellar objects (QSOs) is of fundamental importance to probe the intergalactic medium and address open questions in cosmology. Several approaches have been adopted to find such sources in the currently available photometric surveys, including machine learning methods. However, the rarity of bright QSOs at high redshifts compared to other contaminating sources (such as stars and galaxies) makes the selection of reliable candidates a difficult task, especially when high completeness is required. Aims. We present a novel technique to boost recall (i.e., completeness within the considered sample) in the selection of QSOs from photometric datasets dominated by stars, galaxies, and low-z QSOs (imbalanced datasets). Methods. Our heuristic method operates by iteratively removing sources whose probability of belonging to a noninteresting class exceeds a user-defined threshold, until the remaining dataset contains mainly high-z QSOs. Any existing machine learning method can be used as the underlying classifier, provided it allows for a classification probability to be estimated. We applied the method to a dataset obtained by cross-matching PanSTARRS1 (DR2), Gaia (DR3), and WISE, and identified the high-z QSO candidates using both our method and its direct multi-label counterpart. Results. We ran several tests by randomly choosing the training and test datasets, and achieved significant improvements in recall which increased from similar to 50% to similar to 85% for QSOs with z > 2.5, and from similar to 70% to similar to 90% for QSOs with z > 3. Also, we identified a sample of 3098 new QSO candidates on a sample of 2.6 x10(6) sources with no known classification. We obtained follow-up spectroscopy for 121 candidates, confirming 10(7) new QSOs with z > 2.5. Finally, a comparison of our QSO candidates with those selected by an independent method based on Gaia spectroscopy shows that the two samples overlap by more than 90% and that both selection methods are potentially capable of achieving a high level of completeness.