Machine Learning Techniques for Astrophysics and Cosmology: Photometric Redshifts

The cosmological redshift of a galaxy's light is inferable from its observable properties in images. Because imaging is much easier to acquire than spectroscopic observations that would allow the identification of distinct line features, this motivates the technique of photometric redshift estimation (photo-$z$). Photo-$z$ has been an early and sustained driver for the utilization of artificial intelligence (AI) in astrophysics, and conversely AI methods are underlying most of the recent advances in photo-$z$. Here we review the diversity of AI methods applied to the photo-$z$ problem over the years in a discriminative way, that is, to regress redshift from photometric observables. We argue that, besides optimization suiting specific applications, this approach has effectively converged. It is limited not by the AI methodology but by the size and substantial systematic uncertainties and selection effects in spectroscopic training samples. In order to progress, either an unobtainable quantity and quality of training data or a more principled approach in using it is required. We thus outline ongoing research of integrating AI in a Bayesian modeling of galaxy data. This comes in the form of generative models for representing the distribution of intrinsic properties and outcomes of telescope observations of the galaxy population.