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-z's). 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-z estimations within the photometric ranges derived from the spectroscopic training set. These estimates, however, are not easy to characterize in terms of a photo-z Probability Density Function (PDF), due to the fact that the analytical relation mapping the photometric parameters onto 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-z 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-z's. We present a summary of results on SDSS-DR9 galaxy data, used also to perform a direct comparison with PDF's obtained by the Le Phare SED 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.

The third data release of the Kilo-Degree Survey and associated data products

“…The photometric redshifts are characterized by means of a photo-z Probability Density Function (PDF), derived by the METAPHOR (Machine-learning Estimation Tool for Accurate PHOtometric Redshifts) method, designed to provide a reliable PDF of the error distribution for empirical models (Cavuoti et al 2017). The method is implemented as a modular workflow, whose internal engine for photo-z estimation makes use of the MLPQNA neural network.…”

“…The photometry perturbation can be selected among a series of types, described in Cavuoti et al (2017). Here the choice is based on the following expression, which is applied to the given j magnitudes of each band i as many times as the number of perturbations of the test set:…”

“…Based on this data set, the first scientific results focused on weak lensing studies of galaxies and galaxy A134, page 2 of 26 groups in the Galaxy And Mass Assembly (GAMA, Driver et al 2011) fields (Kuijken et al 2015;Sifón et al 2015;Viola et al 2015;Brouwer et al 2016;van Uitert et al 2016). Furthermore, these data releases were the basis for the first results from a z ∼ 6 quasar search (Venemans et al 2015), a catalogue of photometric redshifts from machine-learning (Cavuoti et al 2015(Cavuoti et al , 2017, preliminary results on super-compact massive galaxies (Tortora et al 2016), and a catalogue of galaxy clusters (Radovich et al 2017).…”

The strong gravitational lens finding challenge

“…These have been used widely for such tasks as handwriting and facial recognition. In astronomy, these families of algorithms are beginning to be used for categorising galaxy morphologies (Dieleman et al 2015), photometric redshifts (Cavuoti et al 2017;Sadeh et al 2016;Samui & Samui Pal 2017), super-nova classification (Lochner et al 2016) and the lens finding problem (Petrillo et al 2017;Jacobs et al 2017;Ostrovski et al 2017;Bom et al 2017;Hartley et al 2017).…”

Estimating photometric redshifts for X-ray sources in the X-ATLAS field using machine-learning techniques

“…SDSS; Beck et al 2016) and optical quasi-stellar objects (QSOs) (e.g. Brescia et al 2015;Cavuoti et al 2017). However, for X-ray AGN, only spectral energy distribution (SED) fitting techniques have been used (Salvato et al 2009;Hsu et al 2014).…”