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pro vyhledávání: '"Math��, Peter"'
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
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5b89452b45371591818b1e053cae03e2
http://arxiv.org/abs/2012.11216
http://arxiv.org/abs/2012.11216
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
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::77946443385c223879debb832a977ee2
https://hal.science/hal-02974206
https://hal.science/hal-02974206
Autor:
Hofmann, Bernd, Math��, 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
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a864f02369a51aa67598f041fb19ef2d
http://arxiv.org/abs/1904.02014
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
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::89722353ab032a0571c62452cb6333a3
http://arxiv.org/abs/1902.05404
http://arxiv.org/abs/1902.05404
This paper studies a Nystr��m type subsampling approach to large kernel learning methods in the misspecified case, where the target function is not assumed to belong to the reproducing kernel Hilbert space generated by the underlying kernel. This
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https://explore.openaire.eu/search/publication?articleId=doi_________::1c4ccfed7e091f858f5c6198124da947
Autor:
Agapiou, Sergios, Math��, Peter
We study Bayesian inference in statistical linear inverse problems with Gaussian noise and priors in Hilbert space. We focus our interest on the posterior contraction rate in the small noise limit. Existing results suffer from a certain saturation ph
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a8f012a6c785ea964e0bc21b3c6641c6
http://arxiv.org/abs/1409.6496
http://arxiv.org/abs/1409.6496
Autor:
Marteau, Cl��ment, Math��, Peter
The authors discuss how general regularization schemes, in particular linear regularization schemes and projection schemes, can be used to design tests for signal detection in statistical inverse problems. It is shown that such tests can attain the m
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Akademický článek
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Autor:
Math, Peter, Tautenhahn, Ulrich
Publikováno v:
Journal of Inverse & Ill-Posed Problems; Dec2011, Vol. 19 Issue 6, p859-879, 21p
Autor:
Blanchard, Gilles, Math, Peter
Publikováno v:
Journal of Inverse & Ill-Posed Problems; 2010, Vol. 18 Issue 6, p701-726, 26p