  The explosion of data in recent years has generated an increasing need for
new analysis techniques in order to extract knowledge from massive datasets.
Machine learning has proved particularly useful to perform this task. Fully
automatized methods have recently gathered great popularity, even though those
methods often lack physical interpretability. In contrast, feature based
approaches can provide both well-performing models and understandable
causalities with respect to the correlations found between features and
physical processes. Efficient feature selection is an essential tool to boost
the performance of machine learning models. In this work, we propose a forward
selection method in order to compute, evaluate, and characterize better
performing features for regression and classification problems. Given the
importance of photometric redshift estimation, we adopt it as our case study.
We synthetically created 4,520 features by combining magnitudes, errors, radii,
and ellipticities of quasars, taken from the SDSS. We apply a forward selection
process, a recursive method in which a huge number of feature sets is tested
through a kNN algorithm, leading to a tree of feature sets. The branches of the
tree are then used to perform experiments with the random forest, in order to
validate the best set with an alternative model. We demonstrate that the sets
of features determined with our approach improve the performances of the
regression models significantly when compared to the performance of the classic
features from the literature. The found features are unexpected and surprising,
being very different from the classic features. Therefore, a method to
interpret some of the found features in a physical context is presented. The
methodology described here is very general and can be used to improve the
performance of machine learning models for any regression or classification
task.
