  Classic embedded feature selection algorithms are often divided in two large
groups: tree-based algorithms and lasso variants. Both approaches are focused
in different aspects: while the tree-based algorithms provide a clear
explanation about which variables are being used to trigger a certain output,
lasso-like approaches sacrifice a detailed explanation in favor of increasing
its accuracy. In this paper, we present a novel embedded feature selection
algorithm, called End-to-End Feature Selection (E2E-FS), that aims to provide
both accuracy and explainability in a clever way. Despite having non-convex
regularization terms, our algorithm, similar to the lasso approach, is solved
with gradient descent techniques, introducing some restrictions that force the
model to specifically select a maximum number of features that are going to be
used subsequently by the classifier. Although these are hard restrictions, the
experimental results obtained show that this algorithm can be used with any
learning model that is trained using a gradient descent algorithm.
