  The signature is a fundamental object that describes paths (that is,
continuous functions from an interval to a Euclidean space). Likewise, the
expected signature provides a statistical description of the law of stochastic
processes. We propose a feature extraction model for time series built upon the
expected signature. This is computed through a Gaussian processes based data
augmentation. One of the main features is that an optimal feature extraction is
learnt through the supervised task that uses the model.
