Recent research suggests that electrophysiological changes develop minutes to hours before the actual clinical onset in focal epileptic seizures. Seizure prediction is a major field of neurological research, enabled by statistical analysis methods applied to features derived from intracranial Electroencephalographic (EEG) recordings of brain activity. However, no reliable seizure prediction method is ready for clinical applications. In this study, we use modern machine learning techniques to predict seizures from a number of features proposed in the literature. We concentrate on aggregated features that encode the relationship between pairs of EEG channels, such as cross-correlation, nonlinear interdependence, difference of Lyapunov exponents and wavelet analysis-based synchrony such as phase locking. We compare L1-regularized logistic regression, convolutional networks, and support vector machines. Results are reported on the standard Freiburg EEG dataset which contains data from 21 patients suffering from medically intractable focal epilepsy. For each patient, at least one method predicts 100% of the seizures on average 60 minutes before the onset, with no false alarm. Possible future applications include implantable devices capable of warning the patient of an upcoming seizure as well as implanted drug-delivery devices.