Forecasting EEG time series with WaveNet
Forecasting electroencephalography (EEG) signals, i.e., estimating future values of the time series based on the past ones, is essential in many real-time EEG-based applications, such as brain-computer interfaces and closed-loop brain stimulation. As these applications are becoming more and more common, the importance of a good prediction model has increased. Previously, the autoregressive model (AR) has been employed for this task -- however, its prediction accuracy tends to fade quickly as multiple steps are predicted. We aim to improve on this by applying probabilistic deep learning to make robust longer-range forecasts. For this, we applied the probabilistic deep neural network model WaveNet to forecast resting-state EEG in theta- (4-7.5 Hz) and alpha-frequency (8-13 Hz) bands and compared it to the AR model. WaveNet reliably predicted EEG signals in both theta and alpha frequencies over 100 ms ahead, with mean errors of 0.8{+/-}0.6 {micro}V (theta) and 0.7{+/-}0.5 {micro}V (alpha), and outperformed the AR model in estimating the signal amplitude and phase. Furthermore, we found that the probabilistic approach offers a way of forecasting even more accurately while effectively discarding uncertain predictions. We demonstrate for the first time that probabilistic deep learning can be utilised to forecast resting-state EEG time series. In the future, the developed model can enhance the real-time estimation of brain states in brain-computer interfaces and brain stimulation protocols. It may also be useful for answering neuroscientific questions and for diagnostic purposes.