Estimation of the masses in the Local Group by Gradient Boosted Decision
  Trees
  Our goal is to estimate the mass of the Local Group (LG) and the individual
masses of its primary galaxies, the M31 and the Milky Way (MW). We do this by
means of a supervised machine learning algorithm, the gradient boosted decision
trees (GBDT) and using the observed distance and relative velocity of the two
as input parameters. The GBDT is applied to a sample of 2148 mock LGs drawn
from a set of 5 dark matter (DM)-only simulations, ran within the standard
$\Lambda$CDM\ cosmological model. The selection of the mock LGs is guided by a
LG model, which defines such objects. The role of the observational
uncertainties of the input parameters is gauged by applying the model to an
ensemble of mock LGs pairs whose observables are these input parameters
perturbed by their corresponding observational errors. Finally the
observational data of the actual LG is used to infer its relevant masses. Our
main results are the sum and the individual masses of the MW and M31: $M_{tot}
= 3.31 ^{+0.79}_{-0.67} $, $M_{MW}=1.15^{+0.25}_{-0.22}$ and
$M_{M31}=2.01^{+0.65}_{-0.39} \ \ \times 10^{12}M_{\odot}$ (corresponding to
the median and the 1st and 3rd quartiles). The ratio of the masses is
$M_{M31}/M_{MW}=1.75^{+0.54}_{-0.28}$, where by convention the M31 is defined
here to be the more massive of the two halos.
