Improved supervised learning methods for EoR parameters reconstruction
  Within the next few years, the Square Kilometer Array (SKA) or one of its
pathfinders will hopefully provide a detection of the 21-cm signal fluctuations
from the Epoch of Reionization (EoR). Then, the main goal will be to accurately
constrain the underlying astrophysical parameters. Currently, this is mainly
done with Bayesian inference using Markov Chain Monte Carlo sampling. Recently,
studies using neural networks trained to performed inverse modelling have shown
interesting results. We build on these by improving the accuracy of the
predictions using neural network and exploring other supervised learning
methods: the kernel and ridge regressions. Based on a large training set of
21-cm power spectra, we compare the performances of these supervised learning
methods. When using an un-noised signal as input, we improve on previous neural
network accuracy by one order of magnitude and, using local ridge kernel
regression, we gain another factor of a few. We then reach a rms prediction
error of a few percents of the 1-sigma confidence level due to SKA thermal
noise (as estimated with Bayesian inference). This last performance level
requires optimizing the hyper-parameters of the method: how to do that
perfectly in the case of an unknown signal remains an open question. For an
input signal altered by a SKA-type thermal noise, our neural network recovers
the astrophysical parameter values with an error within half of the 1$\sigma$
confidence level due to the SKA thermal noise. This accuracy improves to 10$\%$
of the 1$\sigma$ level when using the local ridge kernel regression (with
optimized hyper-parameters). We are thus reaching a performance level where
supervised learning methods are a viable alternative to determine the best-fit
parameters values.
