principle, these techniques can be trivially extended to understand how halo properties map onto different subpopulations of galaxies. This provides a method for making mock catalogs for these different subpopulations as well.

ML algorithms do, however, need to be trained on large, accurate datasets in order for them to learn robust mappings between halo properties and galaxy properties such as $N_{gal}$: a large-volume N-body plus hydro simulation with reliable galaxy formation would be ideal. At present, we have not been able to acquire such a simulation and so we use the Millennium simulation with semi-analytic galaxy formation for this study. However, it is conceivable that such a simulation will become available in the near future which can be used to characterize the halo-galaxy mapping via the ML techniques discussed in this work.

A final point of interest rests in the observation that most HOD methods typically use the halo mass as the only parameter in their halo-to-galaxy mappings. An important topic to study is the sensitivity of $N_{gal}$ to other halo parameters. For example, there have been investigations hinting that the environment of the halo is also an important factor in determining how many galaxies will form (e.g. @Gea05 [@Cea12]). 