The Epoch of Reionization (EoR) was a phase transition from a neutral state to an ionized state where the first generation of luminous objects were able to heat and ionize the surrounding predominantly neutral hydrogen gas. Detection of brightnesstemperature fluctuations from the redshifted hyperfine 21 cm line of neutral hydrogen would provide a direct three-dimensional probe of astrophysics and cosmology during this period. Another important property of reionization is the redshift of its midpoint, when half the hydrogen in the intergalactic medium (IGM) was ionized. This quantity is often estimated by using the cosmic microwave background (CMB) optical depth, tau . Since the optical depth is obtained by integrating along the line of sight, it provides just one number to characterize reionization. As a result, this can be converted into a constraint for the midpoint under the assumption of a parametric form for the ionization history. This is also a probe of the EoR. Upcoming measurements of the high-redshift 21cm signal from the EoR are a promising probe of the astrophysics of the first galaxies and of cosmological parameters. In particular, the optical depth tau to the last scattering surface of the CMB should be tightly constrained by direct measurements of the neutral hydrogen state at high redshift. A robust measurement of $\tau$ from 21cm data would help eliminate it as a nuisance parameter from CMB estimates of cosmological parameters. Previous proposals for extracting tau from future 21cm datasets have typically used the 21cm power spectra generated by semi-numerical models to reconstruct the reionization history. I present in this thesis a different approach which uses convolution neural networks (CNNs) trained on mock images of the 21cm EoR signal to extract tau. I constructed a CNN that improves upon on previously proposed architectures, and perform an automated hyperparameter optimization. I showed that well-trained CNNs are able to accurately predict tau, even when removing Fourier modes that are expected to be corrupted by bright foreground contamination of the 21cm signal. I then began answering a slightly different question that involved raining three different Bayesian models using mock images of ionized fields of hydrogen to extract the ionization fraction of hydrogen by only looks at one redshift to infer the ionization fraction of each simulated image. I showed that for a simple fully Bayesian network it is possible to successfully produces predicted values that are closely aligned with the true values and the model was tuned to find the ``best'' generalized model architecture for this particular problem.