Data-driven, interpretable photometric redshifts trained on
  heterogeneous and unrepresentative data
  We present a new method for inferring photometric redshifts in deep galaxy
and quasar surveys, based on a data driven model of latent spectral energy
distributions (SEDs) and a physical model of photometric fluxes as a function
of redshift. This conceptually novel approach combines the advantages of both
machine-learning and template-fitting methods by building template SEDs
directly from the training data. This is made computationally tractable with
Gaussian Processes operating in flux--redshift space, encoding the physics of
redshift and the projection of galaxy SEDs onto photometric band passes. This
method alleviates the need of acquiring representative training data or
constructing detailed galaxy SED models; it requires only that the photometric
band passes and calibrations be known or have parameterized unknowns. The
training data can consist of a combination of spectroscopic and deep many-band
photometric data, which do not need to entirely spatially overlap with the
target survey of interest or even involve the same photometric bands. We
showcase the method on the $i$-magnitude-selected, spectroscopically-confirmed
galaxies in the COSMOS field. The model is trained on the deepest bands (from
SUBARU and HST) and photometric redshifts are derived using the shallower SDSS
optical bands only. We demonstrate that we obtain accurate redshift point
estimates and probability distributions despite the training and target sets
having very different redshift distributions, noise properties, and even
photometric bands. Our model can also be used to predict missing photometric
fluxes, or to simulate populations of galaxies with realistic fluxes and
redshifts, for example. This method opens a new era in which photometric
redshifts for large photometric surveys are derived using a flexible yet
physical model of the data trained on all available surveys (spectroscopic and
photometric).
