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 (LOO) error is used to quantify unpredictability. On analyzing simulated data sets, we find that structure in data leads to a minimum of the LOO 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 the 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 a probability close to 0,005. the arterial blood pressure signal more regular and thus more predictable, is less effective in patients, and this effect correlates with the seriousness of the heart failure. Using a Gaussian kernel, so that all orders of nonlinearity are taken into account, the leave-one-out error separates controls from patients (probability less than 10−7), and alive patients from patients for whom cardiac death occurred (probability less than 0.01).