Search

We consider the problem of estimating an unknown vector θ from the noisy data Y=Aθ+ε, where A is a known m × n matrix and e is a white Gaussian noise. It is assumed that n is large and A is ill-posed. Therefore in order to estimate θ, a spectral regularization method is used and our goal is to choose a spectral regularization parameter with the help of the data Y. We study data-driven regularization methods based on the empirical risk minimization principle and provide some new oracle inequalities related to this approach. [ABSTRACT FROM AUTHOR]