  Joint feature selection and tree ensemble learning is a challenging task.
Popular tree ensemble toolkits e.g., Gradient Boosted Trees and Random Forests
support feature selection post-training based on feature importances, which are
known to be misleading, and can significantly hurt performance. We propose
Skinny Trees: a toolkit for feature selection in tree ensembles, such that
feature selection and tree ensemble learning occurs simultaneously. It is based
on an end-to-end optimization approach that considers feature selection in
differentiable trees with Group $\ell_0 - \ell_2$ regularization. We optimize
with a first-order proximal method and present convergence guarantees for a
non-convex and non-smooth objective. Interestingly, dense-to-sparse
regularization scheduling can lead to more expressive and sparser tree
ensembles than vanilla proximal method. On 15 synthetic and real-world
datasets, Skinny Trees can achieve $1.5\times$ - $620\times$ feature
compression rates, leading up to $10\times$ faster inference over dense trees,
without any loss in performance. Skinny Trees lead to superior feature
selection than many existing toolkits e.g., in terms of AUC performance for
$25\%$ feature budget, Skinny Trees outperforms LightGBM by $10.2\%$ (up to
$37.7\%$), and Random Forests by $3\%$ (up to $12.5\%$).
