Related papers: Regularization of constrained maximum likelihood i…
This paper presents an inverse reinforcement learning~(IRL) framework for Bayesian stopping time problems. By observing the actions of a Bayesian decision maker, we provide a necessary and sufficient condition to identify if these actions…
This paper deals with Tikhonov regularization for linear and nonlinear ill-posed operator equations with wavelet Besov norm penalties. We focus on $B^0_{p,1}$ penalty terms which yield estimators that are sparse with respect to a wavelet…
We address the inverse problem of cosmic large-scale structure reconstruction from a Bayesian perspective. For a linear data model, a number of known and novel reconstruction schemes, which differ in terms of the underlying signal prior,…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
Fractional Tikhonov regularization methods have been recently proposed to reduce the oversmoothing property of the Tikhonov regularization in standard form, in order to preserve the details of the approximated solution. Their regularization…
From the viewpoint of inverse problem, the optimization of drug release based on the multi-laminated drug controlled release devices has been regarded as the solution problem of the diffusion equation initial value inverse problem. In view…
This paper introduces a novel approach to learning sparsity-promoting regularizers for solving linear inverse problems. We develop a bilevel optimization framework to select an optimal synthesis operator, denoted as $B$, which regularizes…
We study Tikhonov regularization for possibly nonlinear inverse problems with weighted $\ell^1$-penalization. The forward operator, mapping from a sequence space to an arbitrary Banach space, typically an $L^2$-space, is assumed to satisfy…
The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…
Stochastic optimisation algorithms are the de facto standard for machine learning with large amounts of data. Handling only a subset of available data in each optimisation step dramatically reduces the per-iteration computational costs,…
We consider the monotone inclusion problems in real Hilbert spaces. Proximal splitting algorithms are very popular technique to solve it and generally achieve weak convergence under mild assumptions. Researchers assume the strong conditions…
This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to…
This paper explores the incorporation of Tikhonov regularization into the least squares approximation scheme using trigonometric polynomials on the unit circle. This approach encompasses interpolation and hyperinterpolation as specific…
$\ell_1$ regularization is used to preserve edges or enforce sparsity in a solution to an inverse problem. We investigate the Split Bregman and the Majorization-Minimization iterative methods that turn this non-smooth minimization problem…
Tikhonov regularization is a popular approach to obtain a meaningful solution for ill-conditioned linear least squares problems. A relatively simple way of choosing a good regularization parameter is given by Morozov's discrepancy…
We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…
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…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
We consider a modified Tikhonov-type functional for the solution of ill-posed nonlinear inverse problems. Motivated by applications in the field of production engineering, we allow small deviations in the solution, which are modeled through…
In this paper we consider the training of single hidden layer neural networks by pseudoinversion, which, in spite of its popularity, is sometimes affected by numerical instability issues. Regularization is known to be effective in such…