11 citations · 30 across the 8 of their papers we have counts for
9 papers
Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems
Abhishake Rastogi, Gilles Blanchard, Peter Mathé
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. We consider t…
Analysis of regularized Nyström subsampling for regression functions of low smoothness
Shuai Lu, Peter Mathé, Sergiy Pereverzyev
This paper studies a Nyström type subsampling approach to large kernel learning methods in the misspecified case, where the target function is not assumed to belong to the reproduc…
Penalty-based smoothness conditions in convex variational regularization
Bernd Hofmann, Stefan Kindermann, Peter Mathé
The authors study Tikhonov regularization of linear ill-posed problems with a general convex penalty defined on a Banach space. It is well known that the error analysis requires sm…
Bayesian inverse problems with non-commuting operators
Peter Mathé
The Bayesian approach to ill-posed operator equations in Hilbert space recently gained attraction. In this context, and when the prior distribution is Gaussian, then two operators…
Minimax rates for statistical inverse problems under general source conditions
LiTao Ding, Peter Mathé
We describe the minimax reconstruction rates in linear ill-posed equations in Hilbert space when smoothness is given in terms of general source sets. The underlying fundamental res…
Discretized Lavrent' ev regularization for the autoconvolution equation
Steven Bürger, Peter Mathé
Lavrent'ev regularization for the autoconvolution equation was considered by J. Janno in {\itshape Lavrent'ev regularization of ill-posed problems containing nonlinear near-to-mono…