The first analytical expression to estimate photometric redshifts suggested by a machine

TL;DR

This paper introduces the first analytical expression for estimating galaxy photometric redshifts, derived automatically by a machine learning technique called symbolic regression, achieving high accuracy with minimal input data.

Contribution

The paper presents the novel use of symbolic regression to automatically generate an analytical formula for galaxy redshift estimation, a first in cosmology.

Findings

Achieved mean redshift error less than 0.0086 for SDSS galaxies.

Obtained scatter less than 0.045 in redshift estimates up to z~1.0.

Confirmed competitiveness on the PHAT0 dataset.

Abstract

We report the first analytical expression purely constructed by a machine to determine photometric redshifts ($z_{\rm phot}$) of galaxies. A simple and reliable functional form is derived using $41,214$ galaxies from the Sloan Digital Sky Survey Data Release 10 (SDSS-DR10) spectroscopic sample. The method automatically dropped the $u$ and $z$ bands, relying only on $g$, $r$ and $i$ for the final solution. Applying this expression to other $1,417,181$ SDSS-DR10 galaxies, with measured spectroscopic redshifts ($z_{\rm spec}$), we achieved a mean $\langle (z_{\rm phot} - z_{\rm spec})/(1+z_{\rm spec})\rangle\lesssim 0.0086$ and a scatter $\sigma_{(z_{\rm phot} - z_{\rm spec})/(1+z_{\rm spec})}\lesssim 0.045$ when averaged up to $z \lesssim 1.0$. The method was also applied to the PHAT0 dataset, confirming the competitiveness of our results when faced with other methods from the literature. This is the first use of symbolic regression in cosmology, representing a leap forward in astronomy-data-mining connection.