Photometric redshifts for Quasars in multi band Surveys
MLPQNA stands for Multi Layer Perceptron with Quasi Newton Algorithm and it is a machine learning method which can be used to cope with regression and classification problems on complex and massive data sets. In this paper we give the 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 (SDSS, GALEX, UKIDSS and WISE), thus covering a wide range of wavelengths from the UV to the mid-infrared. The method is able i) to achieve a very high accuracy; ii) to drastically reduce the number of outliers and catastrophic objects; iii) 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 DeltaZnorm (i.e. (zspec-zphot)/(1+zspec)), to an average of DeltaZnorm = 0.004, a standard deviation sigma = 0.069 and a Median Absolute Deviation MAD = 0.02 over the whole redshift range (i.e. zspec <= 3.6), defined by the 4-survey cross-matched spectroscopic sample. The fraction of catastrophic outliers, i.e. of objects with photo-z deviating more than 2sigma from the spectroscopic value is < 3%, leading to a sigma = 0.035 after their removal, over the same redshift range. The method is made available to the community through the DAMEWARE web application.