Related papers: Convergence of Regularization Parameters for Solut…
We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…
Deep neural networks exploiting millions of parameters are nowadays the norm in deep learning applications. This is a potential issue because of the great amount of computational resources needed for training, and of the possible loss of…
Generalization is one of the fundamental issues in machine learning. However, traditional techniques like uniform convergence may be unable to explain generalization under overparameterization. As alternative approaches, techniques based on…
Choosing an appropriate regularization term is necessary to obtain a meaningful solution to an ill-posed linear inverse problem contaminated with measurement errors or noise. The $\ell_p$ norm covers a wide range of choices for the…
In this work, our aim is to reconstruct the unknown initial value from terminal data. We develop a numerical framework on nonuniform time grids for fractional wave equations under the lower regularity assumptions. Then, we introduce a…
Regularization is a well studied problem in the context of neural networks. It is usually used to improve the generalization performance when the number of input samples is relatively small or heavily contaminated with noise. The…
A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. However, these so-called filter methods are generally restricted to monotonic transformations,…
In most practical applications such as recommendation systems, display advertising, and so forth, the collected data often contains missing values and those missing values are generally missing-not-at-random, which deteriorates the…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
This paper is concerned with the solution of large-scale linear discrete ill-posed problems with error-contaminated data. Tikhonov regularization is a popular approach to determine meaningful approximate solutions of such problems. The…
The recently developed data-driven eigenmatrix method shows very promising reconstruction accuracy in sparse recovery for a wide range of kernel functions and random sample locations. However, its current implementation can lead to…
In this paper, we aim at recovering an unknown signal x0 from noisy L1measurements y=Phi*x0+w, where Phi is an ill-conditioned or singular linear operator and w accounts for some noise. To regularize such an ill-posed inverse problem, we…
We propose a new stopping criterion for Krylov subspace iterative regularization of large-scale ill-posed inverse problems. Our stopping criterion accurately filters the data using a generalization of the Picard parameter that was…
Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize…
Convergence rates in spectral regularization methods quantify the approximation error in inverse problems as a function of the noise level or the number of sampling points. Classical strong convergence rate results typically rely on source…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
The Singular Value Decomposition is a matrix decomposition technique widely used in the analysis of multivariate data, such as complex space-time images obtained in both physical and biological systems. In this paper, we examine the…
Tikhonov regularization involves minimizing the combination of a data discrepancy term and a regularizing term, and is the standard approach for solving inverse problems. The use of non-convex regularizers, such as those defined by trained…
This paper derives a new class of adaptive regularization parameter choice strategies that can be effectively and efficiently applied when regularizing large-scale linear inverse problems by combining standard Tikhonov regularization and…
Conditional stability estimates require additional regularization for obtaining stable approximate solutions if the validity area of such estimates is not completely known. In this context, we consider ill-posed nonlinear inverse problems…