  Objective. We identify two linked problems related to estimating the phase of
the alpha rhythm when the signal after a specific event is unknown (real-time
case), or corrupted (offline analysis). We propose methods to estimate the
phase prior to such events. Approach. Machine learning is used to mimic a
non-causal signal-processing chain with a purely causal one. Main results. We
demonstrate the ability of these methods to estimate instantaneous phase from
an electroencephalography signal subjected to very minor pre-processing with
higher accuracy than more standard signal-processing methods. Significance.
Phase estimation of EEG-rhythms is a challenge due to non-stationarity and low
signal to noise ratio. The methods presented enable scientists and engineers to
achieve relatively low error by optimizing causal phase estimation on a
non-causally processed signal for a real-time experiments and offline analysis.
