相关论文: Learning a regression function via Tikhonov regula…
This work is concerned with linear inverse problems where a distributed parameter is known a priori to only take on values from a given discrete set. This property can be promoted in Tikhonov regularization with the aid of a suitable convex…
This paper has been withdrawn by the author due to the incorrect application of the divergence theorem to Eqs 7, 8 and 9.
We consider the problem of estimating the slope function in a functional regression with a scalar response and a functional covariate. This central problem of functional data analysis is well known to be ill-posed, thus requiring a…
This paper has been withdrawn by the author due to an error estimate in Lemma 3.1.
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
This paper has been withdrawn
This paper is withdrawn.
This paper has been withdrawn by the author due to a mistake in the section 4.
In this work, we consider ill-posed inverse problems in which the forward operator is continuous and weakly closed, and the sought solution belongs to a weakly closed constraint set. We propose a regularization method based on minimizing…
It is a well-known fact that adding noise to the input data often improves network performance. While the dropout technique may be a cause of memory loss, when it is applied to recurrent connections, Tikhonov regularization, which can be…
This paper has been withdrawn by the authors due to some fatal errors in the analysis.
We withdraw our paper as the factorizability of the correlation functions is unproven.
Nonlocal operators with integral kernels have become a popular tool for designing solution maps between function spaces, due to their efficiency in representing long-range dependence and the attractive feature of being resolution-invariant.…
This paper has been withdrawn.
This paper has been withdrawn because the result turns out to be trivial.
The paper has been withdrawn
This paper has been withdrawn by the author due to the unsure solution to the Dyson-Schwinger equation.
This paper has been withdrawn. See published paper http://arxiv.org/math.HO/0512390
This paper has been withdrawn by the authors, due to a crucial error in beta functions.
Despite recent advances in regularisation theory, the issue of parameter selection still remains a challenge for most applications. In a recent work the framework of statistical learning was used to approximate the optimal Tikhonov…