Tikhonov regularization with oversmoothing penalty for linear statistical inverse learning problems

Rastogi, Abhishake2024-07-122024-07-122019Rastogi, A. (2019). Tikhonov regularization with oversmoothing penalty for linear statistical inverse learning problems. Third International Conference of Mathematical Sciences, Maltepe Üniversitesi. s. 1-4.978-0-7354-1930-8https://aip.scitation.org/doi/abs/10.1063/1.5136221https://hdl.handle.net/20.500.12415/2022In this paper, we consider the linear ill-posed inverse problem with noisy data in the statistical learning setting. The Tikhonov regularization scheme in Hilbert scales is considered in the reproducing kernel Hilbert space framework to reconstruct the estimator from the random noisy data. We discuss the rates of convergence for the regularized solution under the prior assumptions and link condition. For regression functions with smoothness given in terms of source conditions the error bound can explicitly be established.enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessStatistical inverse problemTikhonov regularizationHilbert ScalesReproducing kernel Hilbert spaceMinimax convergence ratesTikhonov regularization with oversmoothing penalty for linear statistical inverse learning problemsConference Object41