  {\it Ab initio\} calculations have been successfully used for evaluating
lattice dynamical properties of solids within the (quasi-)harmonic
approximation (i.e., assuming non-interacting phonons with infinite lifetimes),
but it remains difficult to treat anharmonicity in all but the simplest
compounds. We detail a systematic information theory based approach to deriving
{\it ab initio\} anharmonic force constants: compressive sensing lattice
dynamics (CSLD). The non-negligible terms that are necessary to reproduce the
first-principles calculated interatomic forces are automatically selected by
minimizing the $\ell_1$ norm (sum of absolute values) of the scaled force
constants. By using efficient sampling of the configuration space using a
modest number of atomic configurations with quasi-random displacements, CSLD is
well suited for deriving accurate anharmonic potentials for complex
multicomponent compounds with large unit cells. We demonstrate the power and
generality of CSLD by calculating the phonon lifetimes and thermal transport
properties of Type-I Si clathrates.
