Measuring randomness by leave-one-out prediction error. Analysis of EEG after painful stimulation

A parametric approach, to measure randomness in time series, is presented. Time series are modelled by a kernel machine performing regularized least squares and the leave-one-out error is used to quantify unpredictability. Analyzing simulated data sets, we find that structure in data leads to a minimum of the leave-one-out error as the regularizing parameter is varied. We consider electroencephalographic signals from migraineurs and healthy humans, after painful stimulation and use the proposed approach to detect changes of physiological state and to find differences between the response from patients and healthy subjects. As painful stimulus causes organization of the local activity in cortex, EEG series become more predictable after stimulation. This phenomenon is less evident in patients: the inadequate cortical response to pain in migraineurs separates patients from controls with probability close to $0.005$.