A Machine Learning Approach for Dynamical Mass Measurements of Galaxy
  Clusters
  We present a modern machine learning approach for cluster dynamical mass
measurements that is a factor of two improvement over using a conventional
scaling relation. Different methods are tested against a mock cluster catalog
constructed using halos with mass >= 10^14 Msolar/h from Multidark's
publicly-available N-body MDPL halo catalog. In the conventional method, we use
a standard M(sigma_v) power law scaling relation to infer cluster mass, M, from
line-of-sight (LOS) galaxy velocity dispersion, sigma_v. The resulting
fractional mass error distribution is broad, with width=0.87 (68% scatter), and
has extended high-error tails. The standard scaling relation can be simply
enhanced by including higher-order moments of the LOS velocity distribution.
Applying the kurtosis as a correction term to log(sigma_v) reduces the width of
the error distribution to 0.74 (16% improvement). Machine learning can be used
to take full advantage of all the information in the velocity distribution. We
employ the Support Distribution Machines (SDMs) algorithm that learns from
distributions of data to predict single values. SDMs trained and tested on the
distribution of LOS velocities yield width=0.46 (47% improvement). Furthermore,
the problematic tails of the mass error distribution are effectively
eliminated. Decreasing cluster mass errors will improve measurements of the
growth of structure and lead to tighter constraints on cosmological parameters.
