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We present a new method for inferring photometric redshifts in deep galaxyand quasar surveys, based on a data driven model of latent spectral energydistributions (SEDs) and a physical model of photometric fluxes as a functionof redshift. This conceptually novel approach combines the advantages of bothmachine-learning and template-fitting methods by building template SEDsdirectly from the training data. This is made computationally tractable withGaussian Processes operating in flux--redshift space, encoding the physics ofredshift and the projection of galaxy SEDs onto photometric band passes. Thismethod alleviates the need of acquiring representative training data orconstructing detailed galaxy SED models; it requires only that the photometricband passes and calibrations be known or have parameterized unknowns. Thetraining data can consist of a combination of spectroscopic and deep many-bandphotometric data, which do not need to entirely spatially overlap with thetarget survey of interest or even involve the same photometric bands. Weshowcase the method on the $i$-magnitude-selected, spectroscopically-confirmedgalaxies in the COSMOS field. The model is trained on the deepest bands (fromSUBARU and HST) and photometric redshifts are derived using the shallower SDSSoptical bands only. We demonstrate that we obtain accurate redshift pointestimates and probability distributions despite the training and target setshaving very different redshift distributions, noise properties, and evenphotometric bands. Our model can also be used to predict missing photometricfluxes, or to simulate populations of galaxies with realistic fluxes andredshifts, for example. This method opens a new era in which photometricredshifts for large photometric surveys are derived using a flexible yetphysical model of the data trained on all available surveys (spectroscopic andphotometric).

Data-driven, interpretable photometric redshifts trained on heterogeneous and unrepresentative data