Determining the systemic redshift of Lyman-alpha emitters with neural
  networks and improving the measured large-scale clustering
  We explore how to mitigate the clustering distortions in Lyman-$\alpha$
emitters (LAEs) samples caused by the miss-identification of the Lyman-$\alpha$
(Ly$\alpha$) wavelength in their Ly$\alpha$ line profiles. We use the
Ly$\alpha$ line profiles from our previous LAE theoretical model that includes
radiative transfer in the interstellar and intergalactic mediums. We introduce
a novel approach to measure the systemic redshift of LAEs from their Ly$\alpha$
line using neural networks. In detail, we assume that, for a fraction of the
whole LAE population their systemic redshift is determined precisely through
other spectral features. We then use this subset to train a neural network that
predicts the Ly$\alpha$ wavelength given a Ly$\alpha$ line profile. We test two
different training sets: i) the LAEs are selected homogeneously and ii) only
the brightest LAEs are selected. In comparison with previous approaches in the
literature, our methodology improves significantly both accuracy and precision
in determining the Ly$\alpha$ wavelength. In fact, after applying our algorithm
in ideal Ly$\alpha$ line profiles, we recover the clustering unperturbed down
to 1cMpc/h. Then, we test the performance of our methodology in realistic
Ly$\alpha$ line profiles by downgrading their quality. The machine learning
techniques work well even if the Ly$\alpha$ line profile quality is decreased
considerably. We conclude that LAE surveys such as HETDEX would benefit from
determining with high accuracy the systemic redshift of a subpopulation and
applying our methodology to estimate the systemic redshift of the rest of the
galaxy sample.
