  Linear models, such as force constant (FC) and cluster expansions, play a key
role in physics and materials science. While they can in principle be
parametrized using regression and feature selection approaches, the convergence
behavior of these techniques, in particular with respect to thermodynamic
properties is not well understood. Here, we therefore analyze the efficacy and
efficiency of several state-of-the-art regression and feature selection
methods, in particular in the context of FC extraction and the prediction of
different thermodynamic properties. Generic feature selection algorithms such
as recursive feature elimination with ordinary least-squares (OLS), automatic
relevance determination regression, and the adaptive least absolute shrinkage
and selection operator can yield physically sound models for systems with a
modest number of degrees of freedom. For large unit cells with low symmetry
and/or high-order expansions they come, however, with a non-negligible
computational cost that can be more than two orders of magnitude higher than
that of OLS. In such cases, OLS with cutoff selection provides a viable route
as demonstrated here for both second-order FCs in large low-symmetry unit cells
and high-order FCs in low-symmetry systems. While regression techniques are
thus very powerful, they require well-tuned protocols. Here, the present work
establishes guidelines for the design of protocols that are readily usable,
e.g., in high-throughput and materials discovery schemes. Since the underlying
algorithms are not specific to FC construction, the general conclusions drawn
here also have a bearing on the construction of other linear models in physics
and materials science.
