  In this paper, we consider the nonlinear ill-posed inverse problem with noisy
data in the statistical learning setting. The Tikhonov regularization scheme in
Hilbert scales is considered to reconstruct the estimator from the random noisy
data. In this statistical learning setting, we derive the rates of convergence
for the regularized solution under certain assumptions on the nonlinear forward
operator and the prior assumptions. We discuss estimates of the reconstruction
error using the approach of reproducing kernel Hilbert spaces.
