Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2019
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911829003862016 |
|---|---|
| author | Rastogi, Abhishake Blanchard, Gilles Mathé, Peter |
| author_facet | Rastogi, Abhishake Blanchard, Gilles Mathé, Peter |
| contents | 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, MOR) approach to reconstruct the estimator of the quantity for the non-linear ill-posed inverse problem. The estimator is defined as the minimizer of a Tikhonov functional, which is the sum of a data misfit term and a quadratic penalty term. We develop a theoretical analysis for the minimizer of the Tikhonov regularization scheme using the ansatz of reproducing kernel Hilbert spaces. We discuss optimal rates of convergence for the proposed scheme, uniformly over classes of admissible solutions, defined through appropriate source conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1902_05404 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems Rastogi, Abhishake Blanchard, Gilles Mathé, Peter Statistics Theory Machine Learning 65J20 (Primary) 62G08, 62G20, 65J15, 65J22 (Secondary) 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, MOR) approach to reconstruct the estimator of the quantity for the non-linear ill-posed inverse problem. The estimator is defined as the minimizer of a Tikhonov functional, which is the sum of a data misfit term and a quadratic penalty term. We develop a theoretical analysis for the minimizer of the Tikhonov regularization scheme using the ansatz of reproducing kernel Hilbert spaces. We discuss optimal rates of convergence for the proposed scheme, uniformly over classes of admissible solutions, defined through appropriate source conditions. |
| title | Convergence analysis of Tikhonov regularization for non-linear statistical inverse learning problems |
| topic | Statistics Theory Machine Learning 65J20 (Primary) 62G08, 62G20, 65J15, 65J22 (Secondary) |
| url | https://arxiv.org/abs/1902.05404 |