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Statistical Inverse Problems in Hilbert Scales
In this paper, we study the Tikhonov regularization scheme in Hilbert scales for the nonlinear statistical inverse problem with a general noise.
Inverse learning in Hilbert scales
We study the linear ill-posed inverse problem with noisy data in the statistical learning setting.
Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems
We study a non-linear statistical inverse learning problem, where we observe the noisy image of a quantity through a non-linear operator at some random design points.
Manifold regularization based on Nystr{ö}m type subsampling
In this paper, we study the Nystr{\"o}m type subsampling for large scale kernel methods to reduce the computational complexities of big data.
Optimal rates for the regularized learning algorithms under general source condition
We consider the learning algorithms under general source condition with the polynomial decay of the eigenvalues of the integral operator in vector-valued function setting.
