Photometric Redshifts for Quasars in Multi-band Surveys

Abstract

The Multi Layer Perceptron with Quasi Newton Algorithm (MLPQNA) is a machine learning method that can be used to cope with regression and classification problems on complex and massive data sets. In this paper, we give a formal description of the method and present the results of its application to the evaluation of photometric redshifts for quasars. The data set used for the experiment was obtained by merging four different surveys (Sloan Digital Sky Survey, GALEX, UKIDSS, and WISE), thus covering a wide range of wavelengths from the UV to the mid-infrared. The method is able (1) to achieve a very high accuracy, (2) to drastically reduce the number of outliers and catastrophic objects, and (3) to discriminate among parameters (or features) on the basis of their significance, so that the number of features used for training and analysis can be optimized in order to reduce both the computational demands and the effects of degeneracy. The best experiment, which makes use of a selected combination of parameters drawn from the four surveys, leads, in terms of ∆z <SUB>norm</SUB> (i.e., (z <SUB>spec</SUB> - z <SUB>phot</SUB>)/(1 + z <SUB>spec</SUB>)), to an average of ∆z <SUB>norm</SUB> = 0.004, a standard deviation of σ = 0.069, and a median absolute deviation, MAD = 0.02, over the whole redshift range (i.e., z <SUB>spec</SUB> <= 3.6), defined by the four-survey cross-matched spectroscopic sample. The fraction of catastrophic outliers, i.e., of objects with photo-z deviating more than 2σ from the spectroscopic value, is <3%, leading to σ = 0.035 after their removal, over the same redshift range. The method is made available to the community through the DAMEWARE Web application.