  We explore the interrelationships between the galaxy group halo mass and
various observable group properties. We propose a simple scenario that
describes the evolution of the central galaxies and their host dark matter
halos. Star formation quenching is one key process in this scenario, which
leads to the different assembly histories of blue groups (group with a blue
central) and red groups (group with a red central). For blue groups, both the
central galaxy and the halo continue to grow their mass. For red groups, the
central galaxy has been quenched and its stellar mass remains about constant,
while its halo continues to grow by merging smaller halos. From this simple
scenario, we speculate about the driving properties that should strongly
correlate with the group halo mass. We then apply the machine learning
algorithm the Random Forest (RF) regressor to blue groups and red groups
separately in the semianalytical model L-GALAXIES to explore these nonlinear
multicorrelations and to verify the scenario as proposed above. Remarkably, the
results given by the RF regressor are fully consistent with the prediction from
our simple scenario and hence provide strong support for it. As a consequence,
the group halo mass can be more accurately determined from observable galaxy
properties by the RF regressor with a 50% reduction in error. A halo mass more
accurately determined in this way also enables more accurate investigations on
the galaxy-halo connection and other important related issues, including
galactic conformity and the effect of halo assembly bias on galaxy assembly.
