A sparse regression approach to modeling the relation between galaxy
  stellar masses and their host halos
  Sparse regression algorithms have been proposed as the appropriate framework
to model the governing equations of a system from data, without needing prior
knowledge of the underlying physics. In this work, we use sparse regression to
build an accurate and explainable model of the stellar mass of central galaxies
given properties of their host dark matter (DM) halo. Our data set comprises
9,521 central galaxies from the EAGLE hydrodynamic simulation. By matching the
host halos to a DM-only simulation, we collect the halo mass and specific
angular momentum at present time and for their main progenitors in 10 redshift
bins from $z=0$ to $z=4$. The principal component of our governing equation is
a third-order polynomial of the host halo mass, which models the stellar-mass
halo-mass relation. The scatter about this relation is driven by the halo mass
evolution and is captured by second and third-order correlations of the halo
mass evolution with the present halo mass. An advantage of sparse regression
approaches is that unnecessary terms are removed. Although we include
information on halo specific angular momentum, these parameters are discarded
by our methodology. This suggests that halo angular momentum has little
connection to galaxy formation efficiency. Our model has a root mean square
error (RMSE) of $0.167 \log_{10}(M^*/M_\odot)$, and accurately reproduces both
the stellar mass function and central galaxy correlation function of EAGLE. The
methodology appears to be an encouraging approach for populating the halos of
DM-only simulations with galaxies, and we discuss the next steps that are
required.
