  The recent extension of the Hubble diagram of Supernovae and quasars to
redshifts much higher than 1 prompted a revived interest in non-parametric
approaches to test cosmological models and to measure the expansion rate of the
Universe. In particular, it is of great interest to infer model-independent
constraints on the possible evolution of the dark energy component. Here we
present a new method, based on a Neural Network Regression, to analyze the
Hubble Diagram in a completely non-parametric, model-independent fashion. We
first validate the method through simulated samples with the same redshift
distribution as the real ones, and discuss the limitations related to the
"inversion problem" for the distance-redshift relation. We then apply this new
technique to the analysis of the Hubble diagram of Supernovae and quasars. We
confirm that the data up to $z \sim 1-1.5$ are in agreement with a flat
${\Lambda}CDM$ model with ${\Omega}_M \sim 0.3$, while $\sim 5$-sigma
deviations emerge at higher redshifts. A flat ${\Lambda}CDM$ model would still
be compatible with the data with ${\Omega}_M > 0.4$. Allowing for a generic
evolution of the dark energy component, we find solutions suggesting an
increasing value of ${\Omega}_M$ with the redshift, as predicted by interacting
dark sector models.
