TPZ : Photometric redshift PDFs and ancillary information by using
  prediction trees and random forests
  With the growth of large photometric surveys, accurately estimating
photometric redshifts, preferably as a probability density function (PDF), and
fully understanding the implicit systematic uncertainties in this process has
become increasingly important. In this paper, we present a new, publicly
available, parallel, machine learning algorithm that generates photometric
redshift PDFs by using prediction trees and random forest techniques, which we
have named TPZ. This new algorithm incorporates measurement errors into the
calculation while also dealing efficiently with missing values in the data. In
addition, our implementation of this algorithm provides supplementary
information regarding the data being analyzed, including unbiased estimates of
the accuracy of the technique without resorting to a validation data set,
identification of poor photometric redshift areas within the parameter space
occupied by the spectroscopic training data, a quantification of the relative
importance of the variables used to construct the PDF, and a robust
identification of outliers. This extra information can be used to optimally
target new spectroscopic observations and to improve the overall efficacy of
the redshift estimation. We have tested TPZ on galaxy samples drawn from the
SDSS main galaxy sample and from the DEEP2 survey, obtaining excellent results
in each case. We also have tested our implementation by participating in the
PHAT1 project, which is a blind photometric redshift contest, finding that TPZ
performs comparable to if not better than other empirical photometric redshift
algorithms. Finally, we discuss the various parameters that control the
operation of TPZ, the specific limitations of this approach and an application
of photometric redshift PDFs.
