METAPHOR: a machine-learning-based method for the probability density estimation of photometric redshifts

Abstract

A variety of fundamental astrophysical science topics require the determination of very accurate photometric redshifts (photo-<it>z</it>). A wide plethora of methods have been developed, based either on template models fitting or on empirical explorations of the photometric parameter space. Machine-learning-based techniques are not explicitly dependent on the physical priors and able to produce accurate photo-<it>z</it> estimations within the photometric ranges derived from the spectroscopic training set. These estimates, however, are not easy to characterize in terms of a photo-<it>z</it> probability density function (PDF), due to the fact that the analytical relation mapping the photometric parameters on to the redshift space is virtually unknown. We present METAPHOR (Machine-learning Estimation Tool for Accurate PHOtometric Redshifts), a method designed to provide a reliable PDF of the error distribution for empirical techniques. The method is implemented as a modular workflow, whose internal engine for photo-<it>z</it> estimation makes use of the MLPQNA neural network (Multi Layer Perceptron with Quasi Newton learning rule), with the possibility to easily replace the specific machine-learning model chosen to predict photo-<it>z</it>. We present a summary of results on SDSS-DR9 galaxy data, used also to perform a direct comparison with PDFs obtained by the L<scp>e</scp> P<scp>hare</scp> spectral energy distribution template fitting. We show that METAPHOR is capable to estimate the precision and reliability of photometric redshifts obtained with three different self-adaptive techniques, i.e. MLPQNA, Random Forest and the standard K-Nearest Neighbors models.