Photometric redshifts for the S-PLUS Survey: is machine learning up to
  the task?
  The Southern Photometric Local Universe Survey (S-PLUS) is a novel project
that aims to map the Southern Hemisphere using a twelve filter system,
comprising five broad-band SDSS-like filters and seven narrow-band filters
optimized for important stellar features in the local universe. In this paper
we use the photometry and morphological information from the first S-PLUS data
release (S-PLUS DR1) cross-matched to unWISE data and spectroscopic redshifts
from Sloan Digital Sky Survey DR15. We explore three different machine learning
methods (Gaussian Processes with GPz and two Deep Learning models made with
TensorFlow) and compare them with the currently used template-fitting method in
the S-PLUS DR1 to address whether machine learning methods can take advantage
of the twelve filter system for photometric redshift prediction. Using tests
for accuracy for both single-point estimates such as the calculation of the
scatter, bias, and outlier fraction, and probability distribution functions
(PDFs) such as the Probability Integral Transform (PIT), the Continuous Ranked
Probability Score (CRPS) and the Odds distribution, we conclude that a
deep-learning method using a combination of a Bayesian Neural Network and a
Mixture Density Network offers the most accurate photometric redshifts for the
current test sample. It achieves single-point photometric redshifts with
scatter ($\sigma_\text{NMAD}$) of 0.023, normalized bias of -0.001, and outlier
fraction of 0.64% for galaxies with r-auto magnitudes between 16 and 21.
