  The unprecedented amount and the excellent quality of lensing data that the
upcoming ground- and space-based surveys will produce represent a great
opportunity to shed light on the questions that still remain unanswered
concerning our universe and the validity of the standard $\Lambda$CDM
cosmological model. Therefore, it is important to develop new techniques that
can exploit the huge quantity of data that future observations will give us
access to in the most effective way possible. For this reason, we decided to
investigate the development of a new method to treat weak lensing higher order
statistics, which are known to break degeneracy among cosmological parameters
thanks to their capability of probing the non-Gaussian properties of the shear
field. In particular, the proposed method directly applies to the observed
quantity, i.e., the noisy galaxy ellipticity. We produced simulated lensing
maps with different sets of cosmological parameters and used them to measure
higher order moments, Minkowski functionals, Betti numbers, and other
statistics related to graph theory. This allowed us to construct datasets with
different size, precision, and smoothing. We then applied several machine
learning algorithms to determine which method best predicts the actual
cosmological parameters associated with each simulation. The best model
resulted to be simple multidimensional linear regression. We used this model to
compare the results coming from the different datasets and found out that we
can measure with good accuracy the majority of the parameters that we
considered. We also investigated the relation between each higher order
estimator and the different cosmological parameters for several signal-to-noise
thresholds and redshifts bins. Given the promising results, we consider this
approach as a valuable resource, worth of further development.
