Data augmentation for machine learning redshifts applied to SDSS
  galaxies
  We present analyses of data augmentation for machine learning redshift
estimation. Data augmentation makes a training sample more closely resemble a
test sample, if the two base samples differ, in order to improve measured
statistics of the test sample. We perform two sets of analyses by selecting
800k (1.7M) SDSS DR8 (DR10) galaxies with spectroscopic redshifts. We construct
a base training set by imposing an artificial r band apparent magnitude cut to
select only bright galaxies and then augment this base training set by using
simulations and by applying the K-correct package to artificially place
training set galaxies at a higher redshift.
  We obtain redshift estimates for the remaining faint galaxy sample, which are
not used during training. We find that data augmentation reduces the error on
the recovered redshifts by 40% in both sets of analyses, when compared to the
difference in error between the ideal case and the non augmented case. The
outlier fraction is also reduced by at least 10% and up to 80% using data
augmentation.
  We finally quantify how the recovered redshifts degrade as one probes to
deeper magnitudes past the artificial magnitude limit of the bright training
sample. We find that at all apparent magnitudes explored, the use of data
augmentation with tree based methods provide a estimate of the galaxy redshift
with a negligible bias, although the error on the recovered values increases as
we probe to deeper magnitudes. These results have applications for surveys
which have a spectroscopic training set which forms a biased sample of all
photometric galaxies, for example if the spectroscopic detection magnitude
limit is shallower than the photometric limit.
