Analysing the Epoch of Reionization with three-point correlation
  functions and machine learning techniques
  Three-point and high-order clustering statistics of the high-redshift 21cm
signal contain valuable information about the Epoch of Reionization. We present
3PCF-Fast, an optimised code for estimating the three-point correlation
function of 3D pixelised data such as the outputs from numerical and
semi-numerical simulations. After testing 3PCF-Fast on data with known analytic
three-point correlation function, we use machine learning techniques to recover
the mean bubble size and global ionisation fraction from correlations in the
outputs of the publicly available 21cmFAST code. We assume that foregrounds
have been perfectly removed and negligible instrumental noise. Using ionisation
fraction data, our best MLP model recovers the mean bubble size with a median
prediction error of around 10%, or from the 21cm differential brightness
temperature with median prediction error of around 14%. A further two MLP
models recover the global ionisation fraction with median prediction errors of
around 4% (using ionisation fraction data) or around 16% (using brightness
temperature). Our results indicate that clustering in both the ionisation
fraction field and the brightness temperature field encode useful information
about the progress of the Epoch of Reionization in a complementary way to other
summary statistics. Using clustering would be particularly useful in regimes
where high signal-to-noise ratio prevents direct measurement of bubble size
statistics. We compare the quality of MLP models using the power spectrum, and
find that using the three-point correlation function outperforms the power
spectrum at predicting both global ionisation fraction and mean bubble size.
