  We analyze the practices of reservoir computing in the framework of
statistical learning theory. In particular, we derive finite sample upper
bounds for the generalization error committed by specific families of reservoir
computing systems when processing discrete-time inputs under various hypotheses
on their dependence structure. Non-asymptotic bounds are explicitly written
down in terms of the multivariate Rademacher complexities of the reservoir
systems and the weak dependence structure of the signals that are being
handled. This allows, in particular, to determine the minimal number of
observations needed in order to guarantee a prescribed estimation accuracy with
high probability for a given reservoir family. At the same time, the asymptotic
behavior of the devised bounds guarantees the consistency of the empirical risk
minimization procedure for various hypothesis classes of reservoir functionals.
