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Context. Since the advent of modern multiband digital sky surveys,photometric redshifts (photo-z's) have become relevant if not crucial to manyfields of observational cosmology, from the characterization of cosmicstructures, to weak and strong lensing. Aims. We describe an application to anastrophysical context, namely the evaluation of photometric redshifts, ofMLPQNA, a machine learning method based on Quasi Newton Algorithm. Methods.Theoretical methods for photo-z's evaluation are based on the interpolation ofa priori knowledge (spectroscopic redshifts or SED templates) and represent anideal comparison ground for neural networks based methods. The MultiLayerPerceptron with Quasi Newton learning rule (MLPQNA) described here is acomputing effective implementation of Neural Networks for the first timeexploited to solve regression problems in the astrophysical context and isoffered to the community through the DAMEWARE (DAta Mining & ExplorationWebApplication REsource) infrastructure. Results. The PHAT contest (Hildebrandt etal. 2010) provides a standard dataset to test old and new methods forphotometric redshift evaluation and with a set of statistical indicators whichallow a straightforward comparison among different methods. The MLPQNA modelhas been applied on the whole PHAT1 dataset of 1984 objects after anoptimization of the model performed by using as training set the 515 availablespectroscopic redshifts. When applied to the PHAT1 dataset, MLPQNA obtains thebest bias accuracy (0.0006) and very competitive accuracies in terms of scatter(0.056) and outlier percentage (16.3%), scoring as the second most effectiveempirical method among those which have so far participated to the contest.MLPQNA shows better generalization capabilities than most other empiricalmethods especially in presence of underpopulated regions of the Knowledge Base.

Photometric redshifts with Quasi Newton Algorithm (MLPQNA). Results in the PHAT1 contest