CLAP. I. Resolving miscalibration for deep learning-based galaxy photometric redshift estimation

Obtaining well-calibrated photometric redshift probability densities for galaxies without a spectroscopic measurement remains a challenge. Deep learning discriminative models, typically fed with multi-band galaxy images, can produce outputs that mimic probability densities and achieve state-of-the-art accuracy. However, several previous studies have found that such models may be affected by miscalibration, an issue that would result in discrepancies between the model outputs and the actual distributions of true redshifts. Our work develops a novel method called the C ontrastive L earning and A daptive KNN for P hotometric Redshift (CLAP) that resolves this issue. It leverages supervised contrastive learning (SCL) and $k$-nearest neighbours (KNN) to construct and calibrate raw probability density estimates, and implements a refitting procedure to resume end-to-end discriminative models ready to produce final estimates for large-scale imaging data, bypassing the intensive computation required for KNN. The harmonic mean is adopted to combine an ensemble of estimates from multiple realisations for improving accuracy. Our experiments demonstrate that CLAP takes advantage of both deep learning and KNN, outperforming benchmark methods on the calibration of probability density estimates and retaining high accuracy and computational efficiency. With reference to CLAP, a deeper investigation on miscalibration for conventional deep learning is presented. We point out that miscalibration is particularly sensitive to the method-induced excessive correlations among data instances in addition to the unaccounted-for epistemic uncertainties. Reducing the uncertainties may not guarantee the removal of miscalibration due to the presence of such excessive correlations, yet this is a problem for conventional methods rather than CLAP. These discussions underscore the robustness of CLAP for obtaining photometric redshift probability densities required by astrophysical and cosmological applications. This is the first paper in our series on CLAP.