Abstract
Forecasting electroencephalography (EEG) signals, that is, 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 150 ms ahead, with mean absolute errors of 1.0 1.1 µV (theta) and 0.9 1.1 µV (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 used 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.