Estimating Galaxy Redshift in Radio-Selected Datasets using Machine Learning

All-sky radio surveys are set to revolutionise the field with new discoveries. However, the vast majority of the tens of millions of radio galaxies won't have the spectroscopic redshift measurements required for a large number of science cases. Here, we evaluate techniques for estimating redshifts of galaxies from a radio-selected survey. Using a radio-selected sample with broadband photometry at infrared and optical wavelengths, we test the k-Nearest Neighbours (kNN) and Random Forest machine learning algorithms, testing them both in their regression and classification modes. Further, we test different distance metrics used by the kNN algorithm, including the standard Euclidean distance, the Mahalanobis distance and a learned distance metric for both the regression mode (the Metric Learning for Kernel Regression metric) and the classification mode (the Large Margin Nearest Neighbour metric). We find that all regression-based modes fail on galaxies at a redshift $z > 1$. However, below this range, the kNN algorithm using the Mahalanobis distance metric performs best, with an $\eta_{0.15}$ outlier rate of 5.85\%. In the classification mode, the kNN algorithm using the Mahalanobis distance metric also performs best, with an $\eta_{0.15}$ outlier rate of 5.85\%, correctly placing 74\% of galaxies in the top $z > 1.02$ bin. Finally, we also tested the effect of training in one field and applying the trained algorithm to similar data from another field and found that variation across fields does not result in statistically significant differences in predicted redshifts. Importantly, we find that while we may not be able to predict a continuous value for high-redshift radio sources, we can identify the majority of them using the classification modes of existing techniques.