Objective: This work investigates the hypothesis that focal seizures can be predicted using scalp electroencephalogram (EEG) data. Our first aim is to learn features that distinguish between the interictal and preictal regions. The second aim is to define a prediction horizon in which the prediction is as accurate and as early as possible, clearly two competing objectives. Methods: Convolutional filters on the wavelet transformation of the EEG signal are used to define and learn quantitative signatures for each period: interictal, preictal, and ictal. The optimal seizure prediction horizon is also learned from the data as opposed to making an a priori assumption. Results: Computational solutions to the optimization problem indicate a ten-minute seizure prediction horizon. This result is verified by measuring Kullback-Leibler divergence on the distributions of the automatically extracted features. Conclusion: The results on the EEG database of 204 recordings demonstrate that (i) the preictal phase transition occurs approximately ten minutes before seizure onset, and (ii) the prediction results on the test set are promising, with a sensitivity of 87.8% and a low false prediction rate of 0.142 FP/h. Our results significantly outperform a random predictor and other seizure prediction algorithms. Significance: We demonstrate that a robust set of features can be learned from scalp EEG that characterize the preictal state of focal seizures.