  We use sparse regression methods (SRM) to build accurate and explainable
models that predict the stellar mass of central and satellite galaxies as a
function of properties of their host dark matter halos. SRM are machine
learning algorithms that provide a framework for modelling the governing
equations of a system from data. In contrast with other machine learning
algorithms, the solutions of SRM methods are simple and depend on a relatively
small set of adjustable parameters. We collect data from 35,459 galaxies from
the EAGLE simulation using 19 redshift slices between $z=0$ and $z=4$ to
parameterize the mass evolution of the host halos. Using an appropriate
formulation of input parameters, our methodology can model satellite and
central halos using a single predictive model that achieves the same accuracy
as when predicted separately. This allows us to remove the somewhat arbitrary
distinction between those two galaxy types and model them based only on their
halo growth history. Our models can accurately reproduce the total galaxy
stellar mass function and the stellar mass-dependent galaxy correlation
functions ($\xi(r)$) of EAGLE. We show that our SRM model predictions of
$\xi(r)$ is competitive with those from sub-halo abundance matching and might
be comparable to results from extremely randomized trees. We suggest SRM as an
encouraging approach for populating the halos of dark matter only simulations
with galaxies and for generating mock catalogues that can be used to explore
galaxy evolution or analyse forthcoming large-scale structure surveys.
