Zobrazeno 1 - 10
of 101
pro vyhledávání: '"MÁTHÉ, Péter"'
Autor:
Mathé, Peter, Hofmann, Bernd
The difficulty for solving ill-posed linear operator equations in Hilbert space is reflected by the strength of ill-posedness of the governing operator, and the inherent solution smoothness. In this study we focus on the ill-posedness of the operator
Externí odkaz:
http://arxiv.org/abs/2410.17729
Autor:
Mathé, Peter, Hofmann, Bernd
We introduce a notion of tractability for ill-posed operator equations in Hilbert space. For such operator equations the asymptotics of the best possible rate of reconstruction in terms of the underlying noise level is known in many cases. However, t
Externí odkaz:
http://arxiv.org/abs/2401.09919
Autor:
Hofmann, Bernd, Mathé, Peter
We consider compact composite linear operators in Hilbert space, where the composition is given by some compact operator followed by some non-compact one possessing a non-closed range. Focus is on the impact of the non-compact factor on the overall b
Externí odkaz:
http://arxiv.org/abs/2111.01036
Autor:
Agapiou, Sergios, Mathé, Peter
The Bayesian approach to inverse problems with functional unknowns, has received significant attention in recent years. An important component of the developing theory is the study of the asymptotic performance of the posterior distribution in the fr
Externí odkaz:
http://arxiv.org/abs/2105.10254
The analysis of Tikhonov regularization for nonlinear ill-posed equations with smoothness promoting penalties is an important topic in inverse problem theory. With focus on Hilbert scale models, the case of oversmoothing penalties, i.e., when the pen
Externí odkaz:
http://arxiv.org/abs/2012.11216
Autor:
Rastogi, Abhishake, Mathé, Peter
Publikováno v:
Machine Learning 112, 2469-2499 (2023)
We study the linear ill-posed inverse problem with noisy data in the statistical learning setting. Approximate reconstructions from random noisy data are sought with general regularization schemes in Hilbert scale. We discuss the rates of convergence
Externí odkaz:
http://arxiv.org/abs/2002.10208
We study regularization of ill-posed equations involving multiplication operators when the multiplier function is positive almost everywhere and zero is an accumulation point of the range of this function. Such equations naturally arise from equation
Externí odkaz:
http://arxiv.org/abs/1908.05871
In the setting of supervised learning using reproducing kernel methods, we propose a data-dependent regularization parameter selection rule that is adaptive to the unknown regularity of the target function and is optimal both for the least-square (pr
Externí odkaz:
http://arxiv.org/abs/1905.10764
Autor:
Hofmann, Bernd, Mathé, Peter
We study Tikhonov regularization for certain classes of non-linear ill-posed operator equations in Hilbert space. Emphasis is on the case where the solution smoothness fails to have a finite penalty value, as in the preceding study 'Tikhonov regulari
Externí odkaz:
http://arxiv.org/abs/1904.02014
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. We consider the widely used Tikhonov regularization (or method of regularization, M
Externí odkaz:
http://arxiv.org/abs/1902.05404