Photometric redshifts with Quasi Newton Algorithm (MLPQNA). Results in   the PHAT1 contest
  Context. Since the advent of modern multiband digital sky surveys, photometric redshifts (photo-z's) have become relevant if not crucial to many fields of observational cosmology, from the characterization of cosmic structures, to weak and strong lensing. Aims. We describe an application to an astrophysical context, namely the evaluation of photometric redshifts, of MLPQNA, a machine learning method based on Quasi Newton Algorithm. Methods. Theoretical methods for photo-z's evaluation are based on the interpolation of a priori knowledge (spectroscopic redshifts or SED templates) and represent an ideal comparison ground for neural networks based methods. The MultiLayer Perceptron with Quasi Newton learning rule (MLPQNA) described here is a computing effective implementation of Neural Networks for the first time exploited to solve regression problems in the astrophysical context and is offered to the community through the DAMEWARE (DAta Mining & ExplorationWeb Application REsource) infrastructure. Results. The PHAT contest (Hildebrandt et al. 2010) provides a standard dataset to test old and new methods for photometric redshift evaluation and with a set of statistical indicators which allow a straightforward comparison among different methods. The MLPQNA model has been applied on the whole PHAT1 dataset of 1984 objects after an optimization of the model performed by using as training set the 515 available spectroscopic redshifts. When applied to the PHAT1 dataset, MLPQNA obtains the best bias accuracy (0.0006) and very competitive accuracies in terms of scatter (0.056) and outlier percentage (16.3%), scoring as the second most effective empirical method among those which have so far participated to the contest. MLPQNA shows better generalization capabilities than most other empirical methods especially in presence of underpopulated regions of the Knowledge Base. 
Stefano Cavuoti, Massimo Brescia, Giuseppe Longo and Amata Mercurio
astro-ph.IM astro-ph.CO