Modeling Quasar Photo-$z$ Distribution and Uncertainty. A Study Based on the Kilo-Degree Survey

TL;DR

This study evaluates different neural network models for estimating quasar photometric redshift distributions and uncertainties, emphasizing robustness to data quality variations and the importance of accurate uncertainty modeling.

Contribution

It compares ANN, MDN, and BNN models for quasar photo-$z$ estimation, highlighting the effectiveness of MDNs and BNNs in handling out-of-distribution data and degeneracies.

Findings

MDNs with two Gaussian components perform best among tested models.

BNNs improve out-of-distribution inference but reduce accuracy for bright sources.

Combining data limitations causes significant deviations in redshift reconstruction.

Abstract

We aim to determine the most effective approach for estimating uncertainties in quasar photo-$z$ and to evaluate the ability of different models to reconstruct the true redshift distribution under varying data quality. We use photometric magnitudes from the Kilo-Degree Survey Data Release 5 and spectroscopically confirmed quasars from the Dark Energy Spectroscopic Instrument Data Release 1. We compare artificial neural networks (ANNs), Mixture Density Networks (MDNs), and Bayesian Neural Networks (BNNs), both latter combined with Gaussian Mixture Model (GMM) outputs. To assess robustness to observational limitations, we construct four test sets covering all combinations of sources fainter than those in the training sample and missing photometric bands. ANNs show substantial deviations in reconstructing the redshift distribution. MDNs require at least two Gaussian components to achieve accurate reconstruction, with the three-component MDN providing the best performance in this class. BNNs improve results for sources fainter than the training range, yielding a negative log-likelihood (NLL) gain of $0.11$, but reduce performance for brighter data by $0.07$ NLL. Reconstruction remains feasible for either fainter data or missing magnitudes individually; however, their combination leads to pronounced deviations. Unsupervised clustering identifies two dominant degenerate solutions at redshift pairs of $(1.2, 2.3)$ and $(1.6, 2.5)$. Accurate uncertainty modeling is essential for reliable reconstruction of the redshift distribution directly from photo-$z$. BNNs are particularly beneficial for out-of-distribution inference, although at the expense of reduced accuracy for brighter sources. Our methodology enables the identification and removal of degenerate photo-$z$ estimates unsuitable for tomographic analyses.