  We propose an $\ell_1$-penalized estimation procedure for high-dimensional
linear mixed-effects models. The models are useful whenever there is a grouping
structure among high-dimensional observations, i.e. for clustered data. We
prove a consistency and an oracle optimality result and we develop an algorithm
with provable numerical convergence. Furthermore, we demonstrate the
performance of the method on simulated and a real high-dimensional data set.
