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.