  Identifying a suitable set of descriptors for modeling physical systems often
utilizes either deep physical insights or statistical methods such as
compressed sensing. In statistical learning, a class of methods known as
structured sparsity regularization seeks to combine both physics- and
statistics-based approaches. Used in bioinformatics to identify genes for the
diagnosis of diseases, $\textit{group lasso}$ is a well-known example. Here in
physics, we present group lasso as an efficient method for obtaining robust
cluster expansions (CE) of multicomponent systems, a popular computational
technique for modeling such systems and studying their thermodynamic
properties. Via convex optimization, group lasso selects the most predictive
set of atomic clusters as descriptors in accordance with the physical insight
that if a cluster is selected, so should its subclusters. These selection rules
avoid spuriously large fitting parameters by redistributing them among lower
order terms, resulting in more physical, accurate, and robust CEs. We showcase
these features of group lasso using the CE of bcc ternary alloy Mo-V-Nb. These
results are timely given the growing interests in applying CE to increasingly
complex systems, which demand a more reliable machine learning methodology to
handle the larger parameter space.
