  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.
