Improved supervised learning methods for EoR parameters reconstruction

Within the next few years, the Square Kilometre Array (SKA) or one of its pathfinders will hopefully detect the 21-cm signal fluctuations from the Epoch of Reionization (EoR). Then, the goal will be to accurately constrain the underlying astrophysical parameters. Currently, this is mainly done with Bayesian inference. Recently, neural networks have been trained to perform inverse modelling and, ideally, predict the maximum-likelihood values of the model parameters. We build on these by improving the accuracy of the predictions using several supervised learning methods: neural networks, kernel regressions, or ridge regressions. Based on a large training set of 21-cm power spectra, we compare the performances of these methods. When using a noise-free signal generated by the model itself as input, we improve on previous neural network accuracy by one order of magnitude and, using a local ridge kernel regression, we gain another factor of a few. We then reach an accuracy level on the reconstruction of the maximum-likelihood parameter values of a few per cents compared the 1σ confidence level due to SKA thermal noise (as estimated with Bayesian inference). For an input signal affected by an SKA-like thermal noise but constrained to yield the same maximum-likelihood parameter values as the noise-free signal, our neural network exhibits an error within half of the 1σ confidence level due to the SKA thermal noise. This accuracy improves to 10$\, {\rm per\, cent}$ of the 1σ level when using the local ridge kernel. We are thus reaching a performance level where supervised learning methods are a viable alternative to determine the maximum-likelihood parameters values.