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, such as the characterization of cosmic structures and the weak and strong lensing. Aims: We describe an application to an astrophysical context, namely the evaluation of photometric redshifts, of MLPQNA, which is a machine-learning method based on the quasi Newton algorithm. Methods: Theoretical methods for photo-z evaluation are based on the interpolation of a priori knowledge (spectroscopic redshifts or SED templates), and they represent an ideal comparison ground for neural network-based methods. The MultiLayer Perceptron with quasi Newton learning rule (MLPQNA) described here is an effective computing implementation of neural networks exploited for the first time to solve regression problems in the astrophysical context. It is offered to the community through the DAMEWARE (DAta Mining & Exploration Web Application REsource) infrastructure. Results: The PHAT contest (Hildebrandt et al. 2010, A&A, 523, A31) provides a standard dataset to test old and new methods for photometric redshift evaluation and with a set of statistical indicators that 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 with the 515 available spectroscopic redshifts as training set. 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 that have so far participated in the contest. MLPQNA shows better generalization capabilities than most other empirical methods especially in the presence of underpopulated regions of the knowledge base.