Related papers: Regularized Solutions to Linear Rational Expectati…
In this work, we consider the problem of regularization in the design of minimum mean square error (MMSE) linear filters. Using the relationship with statistical machine learning methods, using a Bayesian approach, the regularization…
The Randomized Kaczmarz Algorithm is a randomized method which aims at solving a consistent system of over determined linear equations. This note discusses how to find an optimized randomization scheme for this algorithm, which is related…
Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, the resulting finite-data problem is ill-posed and admits infinitely many solutions. We propose a numerical method…
Regularized regression problems are ubiquitous in statistical modeling, signal processing, and machine learning. Sparse regression in particular has been instrumental in scientific model discovery, including compressed sensing applications,…
In this paper, we consider the solution of ill-conditioned systems of linear algebraic equations that can be determined imprecisely. To improve the stability of the solution process, we "immerse" the original imprecise linear system in an…
In recent years, functional linear models have attracted growing attention in statistics and machine learning, with the aim of recovering the slope function or its functional predictor. This paper considers online regularized learning…
Numerical computations involving rational matrices often benefit from preserving underlying matrix structures such as symmetry, Hermitian properties, or sparsity that reflect physical, geometric, or algebraic characteristics of the system.…
For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…
Mitigating shortcuts, where models exploit spurious correlations in training data, remains a significant challenge for improving generalization. Regularization methods have been proposed to address this issue by enhancing model…
Calculation of the log-normalizer is a major computational obstacle in applications of log-linear models with large output spaces. The problem of fast normalizer computation has therefore attracted significant attention in the theoretical…
In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…
We consider the two problems of predicting links in a dynamic graph sequence and predicting functions defined at each node of the graph. In many applications, the solution of one problem is useful for solving the other. Indeed, if these…
Inverse problems are characterized by their inherent non-uniqueness and sensitivity with respect to data perturbations. Their stable solution requires the application of regularization methods including variational and iterative…
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…
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…
This work contributes to the development of neural forecasting models with novel randomization-based learning methods. These methods improve the fitting abilities of the neural model, in comparison to the standard method, by generating…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
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…