The Overlooked Potential of Generalized Linear Models in Astronomy-II:
  Gamma regression and photometric redshifts
  Machine learning techniques offer a precious tool box for use within
astronomy to solve problems involving so-called big data. They provide a means
to make accurate predictions about a particular system without prior knowledge
of the underlying physical processes of the data. In this article, and the
companion papers of this series, we present the set of Generalized Linear
Models (GLMs) as a fast alternative method for tackling general astronomical
problems, including the ones related to the machine learning paradigm. To
demonstrate the applicability of GLMs to inherently positive and continuous
physical observables, we explore their use in estimating the photometric
redshifts of galaxies from their multi-wavelength photometry. Using the gamma
family with a log link function we predict redshifts from the PHoto-z Accuracy
Testing simulated catalogue and a subset of the Sloan Digital Sky Survey from
Data Release 10. We obtain fits that result in catastrophic outlier rates as
low as ~1% for simulated and ~2% for real data. Moreover, we can easily obtain
such levels of precision within a matter of seconds on a normal desktop
computer and with training sets that contain merely thousands of galaxies. Our
software is made publicly available as an user-friendly package developed in
Python, R and via an interactive web application
(https://cosmostatisticsinitiative.shinyapps.io/CosmoPhotoz). This software
allows users to apply a set of GLMs to their own photometric catalogues and
generates publication quality plots with minimum effort from the user. By
facilitating their ease of use to the astronomical community, this paper series
aims to make GLMs widely known and to encourage their implementation in future
large-scale projects, such as the Large Synoptic Survey Telescope.
