Quasar photometric redshifts from incomplete data using Deep Learning
  Forthcoming astronomical surveys are expected to detect new sources in such
large numbers that measuring their spectroscopic redshift measurements will be
not be practical. Thus, there is much interest in using machine learning to
yield the redshift from the photometry of each object. We are particularly
interested in radio sources (quasars) detected with the Square Kilometre Array
and have found Deep Learning, trained upon a large optically-selected sample of
quasi-stellar objects, to be effective in the prediction of the redshifts in
three external samples of radio-selected sources. However, the requirement of
nine different magnitudes, from the near-infrared, optical and ultra-violet
bands, has the effect of significantly reducing the number of sources for which
redshifts can be predicted. Here we explore the possibility of using machine
learning to impute the missing features. We find that for the training sample,
simple imputation is sufficient, particularly replacing the missing magnitude
with the maximum for that band, thus presuming that the non-detection is at the
sensitivity limit. For the test samples, however, this does not perform as well
as multivariate imputation, which suggests that many of the missing magnitudes
are not limits, but have indeed not been observed. From extensive testing of
the models, we suggest that the imputation is best restricted to two missing
values per source. Where the sources overlap on the sky, in the worst case,
this increases the fraction of sources for which redshifts can be estimated
from 46% to 80%, with >90% being reached for the other samples.
