  To extract information from the clustering of galaxies on non-linear scales,
we need to model the connection between galaxies and halos accurately and in a
flexible manner. Standard halo occupation distribution (HOD) models make the
assumption that the galaxy occupation in a halo is a function of only its mass,
however, in reality, the occupation can depend on various other parameters
including halo concentration, assembly history, environment, spin, etc. Using
the IllustrisTNG hydrodynamic simulation as our target, we show that machine
learning tools can be used to capture this high-dimensional dependence and
provide more accurate galaxy occupation models. Specifically, we use a random
forest regressor to identify which secondary halo parameters best model the
galaxy-halo connection and symbolic regression to augment the standard HOD
model with simple equations capturing the dependence on those parameters,
namely the local environmental overdensity and shear, at the location of a
halo. This not only provides insights into the galaxy-formation relationship
but, more importantly, improves the clustering statistics of the modeled
galaxies significantly. Our approach demonstrates that machine learning tools
can help us better understand and model the galaxy-halo connection, and are
therefore useful for galaxy formation and cosmology studies from upcoming
galaxy surveys.
