Benchmarking and scalability of machine-learning methods for photometric redshift estimation

Obtaining accurate photometric redshift (photo-z) estimations is an important aspect of cosmology, remaining a prerequisite of many analyses. In creating novel methods to produce photo-z estimations, there has been a shift towards using machine-learning techniques. However, there has not been as much of a focus on how well different machine-learning methods scale or perform with the ever-increasing amounts of data being produced. Here, we introduce a benchmark designed to analyse the performance and scalability of different supervised machine-learning methods for photo-z estimation. Making use of the Sloan Digital Sky Survey (SDSS - DR12) data set, we analysed a variety of the most used machine-learning algorithms. By scaling the number of galaxies used to train and test the algorithms up to one million, we obtained several metrics demonstrating the algorithms' performance and scalability for this task. Furthermore, by introducing a new optimization method, time-considered optimization, we were able to demonstrate how a small concession of error can allow for a great improvement in efficiency. From the algorithms tested, we found that the Random Forest performed best with a mean squared error, MSE = 0.0042; however, as other algorithms such as Boosted Decision Trees and k-Nearest Neighbours performed very similarly, we used our benchmarks to demonstrate how different algorithms could be superior in different scenarios. We believe that benchmarks like this will become essential with upcoming surveys, such as the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST), which will capture billions of galaxies requiring photometric redshifts.