halos (FoF groups) with mass greater than $10^{12}{h^{-1} M_{\odot}}$ (at present, we are unlikely to observe anything less massive except in the local Universe). We then match galaxies from the semi-analytic catalog to these halos, keeping only the primary galaxies of a halo or subhalo (i.e. those flagged 0 or 1 in the Millennium database). Hence, we emerge with a halo catalog listing the following 7 parameters: number of particles in the halo $N_p$, $M_{200}$, velocity dispersion $\sigma_v$, maximum circular velocity $v_{max}$, half-mass radius $R_{1/2}$, spin and number of galaxies in the halo $N_{gal}$. Our goal is to train a machine learning algorithm to predict $N_{gal}$ using the other 6 halo parameters.

The semi-analytic model used to populate the Millennium halos with galaxies is dependent on various thresholds (such as for gas accretion and star formation) that are also evolved through time. This quality makes Millennium an adequate testing ground for ML applications because the mapping from halo parameters to $N_{gal}$ is much more complicated than the straight-forward functions normally employed in methods such as HOD and SHAM. The complexity of these mappings should be closer to the level we expect from actual N-body simulations with hydrodynamics.

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