Compact atomic descriptors enable accurate predictions via linear models.

We probe the accuracy of linear ridge regression employing a 3-body local density representation deriving from the atomic cluster expansion. We benchmark the accuracy of this framework in the prediction of formation energies in molecules, and forces-energies in 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 PCA and LASSO regression for energy fitting on six single-elements datasets. Both methods highlight the possibility to construct a descriptor that is 4 times smaller than the original, with an equal 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 to design material-agnostic, optimally compressed, and accurate, descriptors.