  The identification of descriptors of materials properties and functions that
capture the underlying physical mechanisms is a critical goal in data-driven
materials science. Only such descriptors will enable a trustful and efficient
scanning of materials spaces and possibly the discovery of new materials.
Recently, the sure-independence screening and sparsifying operator (SISSO) has
been introduced and was successfully applied to a number of materials-science
problems. SISSO is a compressed-sensing based methodology yielding predictive
models that are expressed in form of analytical formulas, built from simple
physical properties. These formulas are systematically selected from an immense
number (billions or more) of candidates. In this work, we describe a powerful
extension of the methodology to a 'multi-task learning' approach, which
identifies a single descriptor capturing multiple target materials properties
at the same time. This approach is specifically suited for a heterogeneous
materials database with scarce or partial data, e.g., in which not all
properties are reported for all materials in the training set. As showcase
examples, we address the construction of materials-properties maps for the
relative stability of octet-binary compounds, considering several crystal
phases simultaneously, and the metal/insulator classification of binary
materials distributed over many crystal-prototypes.
