  In this work, we are trying to extent the existing photometric redshift
regression models from modeling pure photometric data back to the spectra
themselves. To that end, we developed a PCA that is capable of describing the
input uncertainty (including missing values) in a dimensionality reduction
framework. With this "spectrum generator" at hand, we are capable of treating
the redshift regression problem in a fully Bayesian framework, returning a
posterior distribution over the redshift. This approach allows therefore to
approach the multimodal regression problem in an adequate fashion. In addition,
input uncertainty on the magnitudes can be included quite naturally and lastly,
the proposed algorithm allows in principle to make predictions outside the
training values which makes it a fascinating opportunity for the detection of
high-redshifted quasars.
