  We probe the accuracy of linear ridge regression employing a three-body local
density representation derived from the atomic cluster expansion. We benchmark
the accuracy of this framework in the prediction of formation energies and
atomic forces in molecules and solids. We find that such a simple regression
framework performs on par with state-of-the-art machine learning methods which
are, in most cases, more complex and more computationally demanding.
Subsequently, we look for ways to sparsify the descriptor and further improve
the computational efficiency of the method. To this aim, we use both principal
component analysis and least absolute shrinkage operator regression for energy
fitting on six single-element datasets. Both methods highlight the possibility
of constructing a descriptor that is four times smaller than the original with
a similar or even improved accuracy. Furthermore, we find that the reduced
descriptors share a sizable fraction of their features across the six
independent datasets, hinting at the possibility of designing
material-agnostic, optimally compressed, and accurate descriptors.
