Morpho-Photometric Redshifts
  Machine learning (ML) is a standard approach for estimating the redshifts of
galaxies when only photometric information is available. ML photo-z solutions
have traditionally ignored the morphological information available in galaxy
images or partly included it in the form of hand-crafted features, with mixed
results. We train a morphology-aware photometric redshift machine using modern
deep learning tools. It uses a custom architecture that jointly trains on
galaxy fluxes, colors and images. Galaxy-integrated quantities are fed to a
Multi-Layer Perceptron (MLP) branch while images are fed to a convolutional
(convnet) branch that can learn relevant morphological features. This split
MLP-convnet architecture, which aims to disentangle strong photometric features
from comparatively weak morphological ones, proves important for strong
performance: a regular convnet-only architecture, while exposed to all
available photometric information in images, delivers comparatively poor
performance. We present a cross-validated MLP-convnet model trained on 130,000
SDSS-DR12 galaxies that outperforms a hyperoptimized Gradient Boosting solution
(hyperopt+XGBoost), as well as the equivalent MLP-only architecture, on the
redshift bias metric. The 4-fold cross-validated MLP-convnet model achieves a
bias $\delta z / (1+z) =-0.70 \pm 1 \times 10^{-3} $, approaching the
performance of a reference ANNZ2 ensemble of 100 distinct models trained on a
comparable dataset. The relative performance of the morphology-aware and
morphology-blind models indicates that galaxy morphology does improve ML-based
photometric redshift estimation.
