  Despite recent advances in regularisation theory, the issue of parameter
selection still remains a challenge for most applications. In a recent work the
framework of statistical learning was used to approximate the optimal Tikhonov
regularisation parameter from noisy data. In this work, we improve their
results and extend the analysis to the elastic net regularisation, providing
explicit error bounds on the accuracy of the approximated parameter and the
corresponding regularisation solution in a simplified case. Furthermore, in the
general case we design a data-driven, automated algorithm for the computation
of an approximate regularisation parameter. Our analysis combines statistical
learning theory with insights from regularisation theory. We compare our
approach with state-of-the-art parameter selection criteria and illustrate its
superiority in terms of accuracy and computational time on simulated and real
data sets.
