Machine-learning computation of distance modulus for local galaxies
  Quickly growing computing facilities and an increasing number of
extragalactic observations encourage the application of data-driven approaches
to uncover hidden relations from astronomical data. In this work we raise the
problem of distance reconstruction for a large number of galaxies from
available extensive observations. We propose a new data-driven approach for
computing distance moduli for local galaxies based on the machine-learning
regression as an alternative to physically oriented methods. We use key
observable parameters for a large number of galaxies as input explanatory
variables for training: magnitudes in U, B, I, and K bands, corresponding
colour indices, surface brightness, angular size, radial velocity, and
coordinates. We performed detailed tests of the five machine-learning
regression techniques for inference of $m-M$: linear, polynomial, k-nearest
neighbours, gradient boosting, and artificial neural network regression. As a
test set we selected 91 760 galaxies at $z<0.2$ from the NASA/IPAC
extragalactic database with distance moduli measured by different independent
redshift methods. We find that the most effective and precise is the neural
network regression model with two hidden layers. The obtained root-mean-square
error of 0.35 mag, which corresponds to a relative error of 16\%, does not
depend on the distance to galaxy and is comparable with methods based on the
Tully-Fisher and Fundamental Plane relations. The proposed model shows a 0.44
mag (20\%) error in the case of spectroscopic redshift absence and is
complementary to existing photometric redshift methodologies. Our approach has
great potential for obtaining distance moduli for around 250 000 galaxies at
$z<0.2$ for which the above-mentioned parameters are already observed.
