Related papers: On truncated spectral regularization for an ill-po…
This paper investigates the convergence properties of spectral algorithms -- a class of regularization methods originating from inverse problems -- under covariate shift. In this setting, the marginal distributions of inputs differ between…
By extending to the stochastic setting the classical vanishing viscosity approach we prove the existence of suitably weak solutions of a class of nonlinear stochastic evolution equation of rate-independent type. Approximate solutions are…
This work deals with the estimation of the extreme value index and extreme quantiles for heavy tailed data,randomly right truncated by another heavy tailed variable. Under mild assumptions and the condition thatthe truncated variable is…
We consider the semilinear stochastic heat equation perturbed by additive noise. After time-discretization by Euler's method the equation is split into a linear stochastic equation and a non-linear random evolution equation. The linear…
When solving rank-deficient or discrete ill-posed problems by regularization methods, the choice of the regularization parameter is crucial. It is also of interest, the regularization norm used in the selection of the solution. In this…
We study for the first time the Cauchy problem for semilinear fractional elliptic equation. This paper is concerned with the Gaussian white noise model for the initial Cauchy data. We establish the ill-posedness of the problem. Then, under…
A nonlinear optimization method is proposed for the solution of inverse medium problems with spatially varying properties. To avoid the prohibitively large number of unknown control variables resulting from standard grid-based…
In this paper we investigate the problem of identifying the source term in an elliptic system from a single noisy measurement couple of the Neumann and Dirichlet data. A variational method of Tikhonov-type regularization with specific…
In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…
When using a finite difference method to solve an initial--boundary--value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze…
A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…
This paper analyzes the effect of a discrete treatment Z on a duration T. The treatment is not randomly assigned. The confounding issue is treated using a discrete instrumental variable explaining the treatment and independent of the error…
Recent quasi-optimal error estimates for the finite element approximation of total-variation regularized minimization problems using the Crouzeix--Raviart finite element require the existence of a Lipschitz continuous dual solution, which…
We propose a new numerical method to solve the linearized problem of travel time tomography with incomplete data. Our method is based on the technique of the truncation of the Fourier series with respect to a special basis of L2. This way…
High-dimensional matrix regression has been studied in various aspects, such as statistical properties, computational efficiency and application to specific instances including multivariate regression, system identification and matrix…
In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…
In this work, we are devoted to the reconstruction of an unknown initial value from the terminal data. The asymptotic and root-distribution properties of Mittag-Leffler functions are used to establish stability of the backward problem.…
Recently, the stochastic asymptotical regularization (SAR) has been developed in (\emph{Inverse Problems}, 39: 015007, 2023) for the uncertainty quantification of the stable approximate solution of linear ill-posed inverse problems. In this…
Estimating the ratio of two probability densities from finitely many samples, is a central task in machine learning and statistics. In this work, we show that a large class of kernel methods for density ratio estimation suffers from error…
We present a regularization method to approach a solution of the pessimistic formulation of ill -posed bilevel problems . This allows to overcome the difficulty arising from the non uniqueness of the lower level problems solutions and…