Feature importance for machine learning redshifts applied to SDSS
  galaxies
  We present an analysis of importance feature selection applied to photometric
redshift estimation using the machine learning architecture Decision Trees with
the ensemble learning routine Adaboost (hereafter RDF). We select a list of 85
easily measured (or derived) photometric quantities (or `features') and
spectroscopic redshifts for almost two million galaxies from the Sloan Digital
Sky Survey Data Release 10. After identifying which features have the most
predictive power, we use standard artificial Neural Networks (aNN) to show that
the addition of these features, in combination with the standard magnitudes and
colours, improves the machine learning redshift estimate by 18% and decreases
the catastrophic outlier rate by 32%. We further compare the redshift estimate
using RDF with those from two different aNNs, and with photometric redshifts
available from the SDSS. We find that the RDF requires orders of magnitude less
computation time than the aNNs to obtain a machine learning redshift while
reducing both the catastrophic outlier rate by up to 43%, and the redshift
error by up to 25%. When compared to the SDSS photometric redshifts, the RDF
machine learning redshifts both decreases the standard deviation of residuals
scaled by 1/(1+z) by 36% from 0.066 to 0.041, and decreases the fraction of
catastrophic outliers by 57% from 2.32% to 0.99%.
